Reviewed and Assembled
April 22, 1996

May 3, 1982

May 11, 1990

Mr. Larry Paulick
National Spa and Pool Institute
200 K Street, N.W.
Washington, D.C.  20006

Re:  Executive Summary of the ADL
        Diving Studies

Dear Larry:

For convenience, I have broken down the Arthur D. Little diving Studies into Studies Number 1-5, the first one being dated June 10, 1974, and the most recent one being dated march 17, 1982.  The first report was prepared at the request of the National Swimming Pool Institute, with the last four being prepared at the request of the National Swimming Pool Foundation.


In the first report, the basic study questions were:

  1. what are the attainable water entrance velocities for a given diver/board combination?

  2. What trajectory can the diver follow after leaving the board?

  3. Following water entry, what will the subject's velocity be as a function of distance and direction travelled underwater?

In order to develope the answers to the above questions strobe light diving photography both in and above the water was used.  Buoyancy studies of the human body along with the development of tow tand drag co-efficience and diving jump characteristics were documented.

In Numbers, this first study stated that from either a dive from a one meter board or a running dive from the deck, water entrance velocities of form 20 to 22 feet per second can be obtained.  At a water depth of 10 feet, the diver is still travelling approximately 5 feet per second.  Lowering the diving board from one meter to one-half meter decreased this velocity by only 15 percent.

At that point in time, there was no agreed upon "safe" impact velocity for hitting one's head on the bottom or sides of the pool. Later studies revealed potentially dangerous velocity to be in the range of 2 to 3 feet per second.

The basic findings of this first study concluded that

"Within practical limits of pool design, depth for either a running dive or from a spring or jump board of one meter height, it is not possible to rely only on the slowing effect of -.the water to assure" that the diver will not impact the bottom of the pool at dangerous velocities."

The first study clearly called for additional studies in the hopes of providing an increased margin of safety for recreational diving. The National Swimming Pool Foundation undertook the funding of these additional studies.

A portion of this report entitled "Summary, Findings and Conclusions" consisting of 21 pages is attached hereto for reference.


Arthur D. Little's Study Number 2 launched in 1977 and completed on May 15, 1980 endeavored to find out why diving accidents indeed do happen at all. The figures in Study Number 1 would tend to indicate that 20 to 22 feet of water depth would be required to insure safe diving from a one meter board. With millions of dives each year resulting in only a few accidents, although severe in several cases, it was obvious that. the diver must. do something to protect himself rather than rely on the slowing effects of the water. Consequently, Study Number 2 concentrated on endeavoring to determine the mode of the accident as well as endeavoring to establish the human factors surrounding the accident..

This study indicated that, of approximately 4,000 nationwide. annual spine injury accidents, 12.5% resulted from diving. Of this 12.5%, half of these resulted in quadriplegia. Of those accidents resulting in, quadriplegia, only one out of four occuring in swimming pools, with the other three occurring in the natural aquatic environment. Further, of those one out of four occurring pools, only one out of twenty of these occurred in the diving portion of the pool. Although originally when the study was done, it was assumed that the accidents were diving board related, it was now revealed that three out of four of those accidents were not even related to the swimming pool, and of those that are related to the pool, 90-95% occur in the shallow portions of the pool.

The study also revealed that 85% of all diving accidents occur to males within the age bracket of 13-23.

One of the recommendations from this study was to teach children safe diving in the controlled environment of institutional and residential pools before they reach the "dangerous" years.

In relation to this second study I have attached 6 pages from this study beginning with "Chapter 1 - Findings" through "Chapter 2 Recommendations."

Incidentally, this second study was almost as lengthy as the first study, and indeed began to open up new avenues of thought if the industry was sincerely interested in endeavoring to reduce diving accidents. Assuming that somehow, magically, all pools could be made 22 feet in the diving portion thereof, the real reduction in serious diving injuries would amount to slightly over 1% (5% occurring in the deep end times 25% occurring in pools). This leaves roughly 98% of the accidents occurring in the shallow portions of the pool and the natural aquatic environment. Clearly, the opportunities for reducing these serious accidents appear to be in the area of safe diving training regardless of the environment (pools or natural) and almost regardless of the depth (shallow or deep).


Report Number 3 was a little bit of a side-step from the prior two programs in that it considered diving board heights of one and three meter, whereas the original two studies covered the residential diving board heights up to and including one meter only. We wished to be reasonably certain that the same basic underwater trajectories and so forth applied to these boards as well. Further, there was consideration by the American Public Health Association at about this time to create an immensly large diving hopper from a three meter board. From all the information we had thus far from Arthur D. Little, it appeared that such an extremely large diving hopper would be to no avail.

This study seemed to indicate that the current NSPI three meter diving hopper geometry was somewhat consistent with the hopper geometry selected for the lower boards; i.e. it was progressively larger as based upon underwater velocities as related to a new component added to the matrix of diving-underwater-steering.

Although this third study was primarily created in order to provide information to the American Public Health Association, it did result in meaningful input to the overall program by the development of the constant radius steering curves generated by Dr. Stone.

Dr. Stone's 6 page letter of December 19, 1980, which in itself is this third report is attached hereto for reference. The drawings referred to in this letter are not attached inasmuch as their size makes it difficult to reproduce, and a final study generated a more concise set of curves.


The Fourth Study, dated October, 1981, went one step further in generating. steering curves underwater. In lieu of the constant radius concept, a new concept of constant~ force, ie, constant steering effort, was generated in this report. The thought here being that the diver is not truly aware of the radius, but he is aware of the effort to change direction, and, assuming that the level of his effort is the same for varying board heights, are we providing sufficient water in each case to accomodate the required underwater trajectory? This report makes a further comparison between the proposed APHA diving hopper geometry and the proposed NSPI geometry and, although it continues to mention the radius of the steering circle," the concept of constant effort is clearly being developed.

6 pages from this report are included herewith, beginning with "A Rationale for Rating Pools with Diving Boards" Introduction through Summary of Results.


Finally what I have chosen to call Arthur D. Little's Report Number 5, simply for purposes of trying to keep these various documents clear in my own mind, consists of only a letter of March 17, 1982, along with four large blueprints referred to in the letter.

This study now concentrates on an initial 3-0 steering force as a result of the diver making use of his hands, arms, lifting his head and arching his back, this initial steering force of 3-G followed by a circular path of constant radius is more or less shown on the attached drawings of pool types II - V. The 3-G steering force line shown on these drawings represents the maximum approach of a diver's body to the pool bottom when maintaining an initial 3-G steering force, regardless of whether the dive was an almost vertical one, or a dive far out into the pool, ie, the distance between the 3-G steering force line and the geometry line shown on these drawings represents the clearance available. Incidentally, at the time this geometry was developed, the proposed NSPI bottom slopes for the 1982 standards were being considered. This study resulted in the Technical Council's acceptance of a recommendation for the new 3 in 1 maximum upslope from the deep end. As you can see from these drawings, this new upslope proposed NSPI (March, 1982) provides a more consistent clearance relationship between the 3-G steering force and the pool bottom.

I have attached the entire letter of March 7, 1982, which represents the fifth report.

From one point of view, this letter, more or less, states that the geometry we have proposed (as well as that in the past) is reasonably consistent with a 3-G steering force, that a 3-G steering force is not at all unusual to expect of a diver, and that there are no surprises in the proposed designs, assuming that the diver makes an essentially constant steering effort.

For the moment, at least, this would appear to be the end of this series of studies, culminating in a much better understanding of diving geometry, and resulting in slightly modified underwater pool profiles in the suggested industry standards.

Again, though, it should be pointed out that an overwhelming percentage of serious diving injuries occur in areas other than the deep end or deep portion of the pool. It is this knowledge that leads the National Swimming Pool Foundation to hope that, with the assistance of the National Spa & Pool Institute, significant strides can be made in diving safety through diver education at all levels. Efforts are now moving forward in this regard, via the preparation of a one page diving instruction handout sheet, and the development of a short diving training film that, it is hoped, can be included in the physical education programs nationwide.


Leif Zars

ADL Summary


In Order to assess the relative risk associated with the two alternative designs for the Type II pool, comparisons were make under three differing steering assumptions.

  1. Marginal upward steering

  2. No steering effort (straight line underwater trajectory)

  3. Steering down rather than up

It was also necessary to compare the results of these three steeering errors in three separate areas of the pool:

  1. In the area where the variable slope option has a 1:2.5 slope, the suggested pool has a 1:3 slope and the two pools have a comparable depth.

  2. In the area where the variable slope option has a 1:1 slpe and is deeper than the suggested pool.

  3. In the area of maximum depth where the variable slope has a flat bottom and is deeper tha the suggested pool.

As a result of thepreceding analysis, Dr. Stone made the following comments:

the design basis for the springboard diving area of a pool shoud be to provide a water envelope that allows a diver to safely and  comfortably maneuver underwater to regain the surface with reasonable upward steering effors.

the design should be such that marginal steering errors, should not result in a radical change in thedegree of risk associated with a dive.

a designercan provide a safe pool for divers who will steer properly.   Common sense dictates that if you dive straight to the bottom of a pool and don't protect yourself, you will get hurt.  it is no more possible to design a pool to protect a diver who won't steer properly than it is to design a highway for a driver who won't steer properly.


Comparison of NSPI Type II pool and the California modification of this type of pool.  Various pool measurements were compared and Dr. Stone opined, that upslope angle is more critical in design for safety than marginal increases in depth.   In a trade-off, he would favor reducing the upslope over locally increasing the depth at the deepest point in the pool.

In comparing transverse sections of the two pools, Dr. Stone concludes that meither of the pools is designed for deck dives across the pool.  he believes that the risk of hitting the opposite wall is obvious; the Type II pool provides some additional safety margin over the California modification but only at the widest point in the pool.


Suggested NSPI pool geometries based on two assumptions:

  1. Lowering the board should reduce the diver's speed at entry and shorten his trajectory in air, thus reducing the requirements for underwater maneuvering space.

  2. Shortening the board shoud have lower efficiency and reduce the diver's takeoff speed, thus reducing entry speed and shortening the trajectory in air, thus further reducing requirements for underwater maneuvering space.

The first assumption is valid and magnitude of the changes can be calculated directly, relying only on the law of gravity.

The suggestion of a generic pool shape that is scaled in size in relationship to diving board parameters is a good one; however, the only board parameters addressed so far are height and length.  The lowering of the board helps to some degree, but this effect by itself still leaves a situation where the smaller pools demand significantly more of a diver that the larger pool with higher and longer boards.

Beleives objectives should be that all pool demand approximately the same performances of the diver.  To accomplish this, he suggests that both board efficiency and height be specified in relation to diving geometry.

From analysis, the absolute necessity for steering up and to steer up immediately following water entry is clearly demonstrated.  Ultimately may want to establish a performance criteria based on time to the bottom, sterring radius and force.


As a result of this analysis, it is suggested that the design basis for springboard diving area of a pool should be to provide a water envelope that allows a diver to safely and comfortably maneuver underwater to regain the surface with reasonable upward steering effort.

The design should be such that marginal steering errors should not result in a radical change in the degree of risk associated with the diver.


Calculations performed for "worst case" diver to determine how far a diver can go and how fast he will be going when he gets there in a dive from a pool deck as well as and estimate of the distance required to slow the diver to the point where direct impact with the far wall of the pool could be tolerated.

In regard to the second aspect, Dr. Stone states that in a direct impact, the motion of the arms, shoulders and legs can continue essentially undiminished over the duration of the impact; thus the accelerated mass is equal to or less than half the total mass of the diver.  Under the assumptions outlined here, one concludes that in a direct impact with a pool wall a 200 pound man is potentially at risk of suffering a compression fracture of the cervical spine if the impact occurs at speeds above 6 to 8 feet per second.  These speeds translate into horizontal distances of 15 to 18 feet from the point of takeoff.

It is possible to predict how fast a diver will be going after he has travelled a given distance on the basis of two calculations.  These are the diver's trajectory in air and his trajectory underwater.

on the basis of a close correspondence between the theory develped and experimentation, it was concluded that the theoretical development correctly predicts speed as a function of distance travelled.

ADL 9B - Springboard Diving Area Configuration Study

An analysis of springbarod diving into pools of differing size and shape.   It is not possible to rely solely on distance travelled through water, in a pool with practical dimensions, to slow a diver to the point where he can suffer head impact with the bottom at a steep angle without risk of serious injury.  In all cases, it is necessary for the diver to "steer up," that is, to direct his motion back toaward the surface to avoid bottom contact.

Common sense and experience dictates that a diver that chooses to can dive to the bottom of any pool.  If he doesn't protect his head when he gets there, he can get hurt.

There are design optimization criteria that lead to a specification of the depth and shape of a reaasonably safe diving area for those divers that attempt to steer properly.  They are:

  1. The springboard diving area in any pool should have a configuration defined by depth and bottom slope that requires essentially the same sterring effor independent of whether a dive is very steep or one that projects the diver far out into the pool.

  2. As the mounting height of the springboard is changed, there should be a corresponding change in the depth and size of the diving area so that the steering effort required for safe maneuver from one type of pool to another is not significantly changed.


        Pool Shape:  a review of individual figures for the suggested NSpI Type I through Type V pools show that there is a close correspondence between the specified pool shapes and the corresponding contours of constant steering effort.  The design for each type of pool appears to be balance in that the margin of safety is nearly constant independent of type of forward dive performed.

        Bottom Slope:  over the expected range of forward springboard dives, the suggested pool shapes correspond closely to the indicated cntours of constant steering effort.

        Pool Size:  in light of the nearly constant initial steering acceleration, it appears that the design progression fom the Type I through Type V pool comes very close to satisfying the second suggested design optimization criterion.  There appears to be little change in the steering force required for safe maneuvering form one type of pool to the next.

        The range of initial steering acceleration required to attain the permissible steering radii is well within the capability of the recreational diver.

        The range of pool designs that have evolve within the NSPI over the years closely approximate the shpe, size, and depth that results when one considers contours of constant steering effort.  In addition, the initial steering acceleration or force required in the differenttypes of suggested pools is nearly constant.  It would appear that the suggested designs come close to fully satisfying the two design optimization criterion suggested above.

ADL 10 - Diving Rock Installations

An analysis of standing dives from diving rocks installed at different heights above water.  Just as there were in the case of springboard diving, there are other considerations that lead to the specification of the depth and shape of a reasonably safe diving area for a diving rock installation for divers who attempt to steer properly:

  1. The diving area associated with a particular diving rock installation shoud have a configuration defined by depth and bottom slope that requires essentially the same steering effort independent of whether a dive is very steep or one that projects the diver far out into the pool.

  2. As the height of the diving rock above water is changed, there should be a corresponding change in the depth and size of the associated diving area so that the steering effort required for safe maneuver from one type of installation to another is not significantly changed.

To determine the depth and shape requirements for diving rocks mounted at different heights above water, a series of calculations were carried out. These calculations were of the trajectories in air and underwater for a "worst case" diver when diving rocks are mounted at 1.0, 2.0 and 3.0 feet above water.

The "worst case" diver considered in these calculations would require ..a water 'depth of five feet in front of a diving rock with mounting heights of up to three feet above water under, the condition that he not make a "dive with a takeoff angle greater than 75 degrees with respect to the horizontal and that he steer a radius of three feet after his head has penetrated a distance of 2.4 feet following entry.

If one accepts a three foot steering radius as maximum permissible steering radius, the "worst case" diver considered in these calculations requires a water depth of five feet for diving rocks mounted up to three feet above water.

        Bottom Slope:  unlike the springboard diving case where it-was found that contours of constant steering effort had a nearly constant 1:5 slope independent of diving board mounting height, the contour slope in the case of diving rocks varies quite rapidly with the height of the diving rock above water. This slope is 1:2.5 for a-diving rock mounted 11-0.11 above water and 1:4 for a diving rock mounted 3'-0" above water.


What is the minimum surface area that ought to be provided to accommodate diving from a diving rock 3'-0" above water?

Horizontal surface area in. front of a diving rock. is that provided by limiting lines of 45 0 to the axis of the diving rock or to the surface area provided in front of a point on the pool wall directly below the diving board in a Type II pool out to a distance of 18 feet from face of the rock, whichever is less.

At what point should the 1:4 upslope begin to accommodate diving from a diving rock 31-0" above water?

The 1:4 upslope can begin at a distance of 8'-0" from the face of the diving rock. It was suggested to act conservatively and make an interim recommendation of a depth of 6'-0" for the 3'-O" high diving rock diving rock, thereby accommodating a 4'-0" turning radius.

ADL 11

ADL 11 was to be "Divers Steering Ability" - now being evaluated as "Underwater Steering Study" and identified as First Lexington #2.

ADL 12 - Diving Board Rating Study

(performed by First Lexington Group, and identified as First Lexington. #1)

In order to accomplish the objective of developing a practical and effective method of rating. the performance of diving boards by measuring the physical characteristics that determine the performance of divers on these boards and to relate these characteristics to actual diving experiences, the First Lexington Group focused on four tasks:

The experimental research and theoretical analysis that are the basis of the report show that diving boards act as resonant energy storage devices. This finding. must reflect on how one thinks about the performance of the combination of diver and diving board and how one rates this performance.

At the conclusion of the study, the following recommendations were made:

Rating system

On the basis of the results obtained in the research that serves as the basis for this report, it is clear that a diving board rating system based principally on the length of a diving board is no longer adequate. For this reason, it is recommended that a new "performance based diving board rating system" is required. This new rating system should be based principally on the measured spring constant of the diving board-mounting combination under consideration. In addition to the spring constant, the rating system should continue to utilize the mounting height above water at a rating criteria.

Mounting constraints

In view of the ever increasing number of spring mounting devices available for diving boards and. the profound effect that these mountings can have on board performance, it is recommended that manufacturers vary the mounting hole spacing on those boards that are designed to be mounted on a particular spring device. In this way it should be possible to assure that a particular board is mounted in accordance with the manufacturer's design intent.

If someone were to choose to redrill a board to mount it onn some other type of mounting than the one intended by the manufacturer, hter is little or nothing that can be done to prevent such and action.  However, such an action would now require a physical modification of the board before it could be mounted.

Measurement method

The word done in this research program shows that the measurement of diving board characteristics by means of dynamic loading experiments provides a fast and accurate method for determining the physical parameters that determine performance and that are required for making appropriate rating judgements.  It is therefore recommended that diving board rating information shoud be obtained by dynamic loading experiments of the type described in this report.

Further investigation recommended that board installations be rated on the basis of the "equivalent fall height" for a given installation.  Equivalent fall height is the distance that a diver's center-of-gravity would have to fall, from rest, to attain a water entry speed equal to the speed that can be attained by a skilled professional diver when diving from the board installation being rated.

Using the equivalent fall height as a basis for rating provides a simple, meaningful and direct measure of the potential performance of a diver when diving from a given board installation.  This quantity determines in a very direct way:

ADL 13 - Review of Technical Material Related to Swimming Pool Design and Diving Safety by Dr. Stone.

This study was for the review of the 22 documents on the attached list (Attachment B) and for a verbal report to be given to the U.S. CPSC - which was done.   Basically Dr. Stone found nothing in these documents to change any of his prior work.

First Lexington #1 - See ADL #12

First Lexington #2 - "Underwater Steering Study" presently being performed by Dr. Stone at First Lexington Group.

ADL 1 - Attachment




On the basis of the theoretical development in Section IV of this report, we conclude that tall athletic individuals are capable of attaining slightly higher water entry velocities than shorter, less muscular individuals when diving from the deck, from a platform, or from a diving or jump board of a given height. In addition, again for theoretical reasons outlined in Section IV, these same individuals slow down less rapidly underwater than shorter, stouter individuals, unless they intentionally do something to reduce their speed. The tall, thin athletic individual therefore physically represents a worst case risk in terms of attaining and maintaining high velocities underwater.

We find that reasonably athletic young men when diving from a one meter board enter the water with nearly constant velocity in the order of 20 to 22 feet per second. Following entry of the head into water, there is a transition distance equal to approximately 40 percent of the subject's height in which the velocity remains essentially constant as the effects of increasing drag and buoyant force tend to negate the acceleration that would occur, if only gravity were acting. Following this transition region the diver's underwater speed is seen to decrease exponentially. In the case of tall individuals (-6 feet) with low drag coefficients who hold a diving configuration underwater, it is found that their speed is decreased by a factor of two for each additional eight feet that they travel. That is, after the head is two feet underwater, they are travelling at -20 feet/second; at 10 feet they are travelling at 10 feet/second; at 18 feet, they would be travelling at -5 feet/second.

Both entry speed and speed vs distance travelled underwater have been studied in detail. It was also found that one can attain entry speed of the same magnitude (-20 feet/second) by making a running approach over the pool deck. Lowering the diving board from one meter to a half meter decreases entry velocity by only 15%.

    At this point in time, there is no agreed upon, "safe" velocity for head impact with the bottom or sides of a pool.   However, from our measured velocities, we conclude that, for either a running dive or a dive from a diving board or jump board, the primary protective mehanism must be the action of the diver rather than the slowing effects provided by the passage of his body through water.  We have repeatedly observed a number of subjects at a speed of 8 feet/second or higher after travelling a distance of 12 feet or more underwater.  In almost all cases our test subjects bottomed in the M.I.T. pool at a depth of 123 feet without their attempting to do so.  Their only instruction was to hold a good diving configuration.  Their protective response in these cases was to push off the bottom with their hands.

To reiterate our basic findings, we conclude that:

"Within practical limits of pool design depth for either a running dive or from a spring or jump board of 1 meter height, it is not possible to rely only on the slowing effect of the water to assure that the diver will not impact the bottom of the pool at dangerous velocities."

ADL 2 - Attachment



It is of the utmost importance that efforts to reduce the incidence of serious injury in swimming pools, and in the natural aquatic environment, focus on central causes rather than on less important related issues if these efforts are to make a major contribution to improved aquatic safety. To this end, it was necessary in this study to determine who suffers serious injury in aquatic activities: where, when, and under what circumstances do these injuries occur? How do they occur, and most important, what can be done to reduce the frequency of severe injury? Engineering changes and improved training methods must be devised and implemented where appropriate. This study is seen as a significant step in this direction. The findings and results from this study are presented below.

1.1 Statistical Findings

This study produced the following statistical findings:

    Analysis of the available data on injury to the cervical spinal cord provide insights into who has this type of accident and where the accident occurs. Specifically, the findings indicate that:

1.2 Physical Findings

    On the basis of data obtained from experiments, analysis, and review of relevant scientific literature performed as part of the study, it was found that:

1.3 Central Findings

    The central finding of this study is that only a very small fraction of the diving accedents resulting in spinal injury involve a dive from a diving board into the deep diving area of the pool.  The greatest number of diving accedents occur as a result of a dive into shallow water, primarily in the natural aquatic environment rather than i pools.  These accidents overwhelmingly involve young adult males during the "dagerous years" from 13 to 23.  Children below the age of 13, during the "safe years," have 100 times fewer cervical spinal cord injuries than teenagers.

    The study show that the principal focus for activities in diving safety, by the National Swimming Pool Foundation, shoud be the reduction of the incidence of spinal injury in diving.  This can best be accomplished through the use of the controlled environments such as institutional and residential pools to teach preteenagers how to dive into shallow water during the "safe years."  If the teaching is done effectively and continued as the divers become teenagers and enter the "dangerous years," they will be equipped with the basic skills required to dive safely in the natural aquatic environment as well as in pools.



As a result of the study findings, the following recommendations are made:

2.1 Engineering

    The primary technical finding of this study is that the most probable cause of injury to the cervical spine in diving, Is that the diver may hit his head on the bottom while traveling at a steep enough angle of approach to constrain the subsequent motion of his head to rolling on the bottom without slipping. If the angle of approach is steeper than the critical angle for slip, the rolling of the head on the bottom forces the cervical spine in the direction of maximum flexion. The cervical spine can be injured by an applied force as small as 300 pounds. This level of force is generated by bottom contact speeds of only a few feet per second for most individuals.

    No practical way has been found to reduce a diver's speed to the point where he can safely risk contact of the head with the bottom, at angles greater than the critical angle for slip on the bottom, and no practical engineering way has been devised to control a diver's underwater trajectory.

    It is most important to construct the diving area in a pool so that the diver's head will slip on the bottom following contact. This is particularly true in those areas where it is likely that a diver might contact the bottom at a steep angle of approach. In the course of this work, the slip characteristics of common pool finishes including tile, painted concrete, and vinyl were measured. It was found that the critical angle for slip of these finishes measured against human hair was typically 65 degrees with little variation from one finish material to another.

All of these finishes were found to be equally slippery.

    More slippery pool finish materials, in those areas of a pool where the depth is greater than a diver's height, may reduce the incidence of spinal cord injury in the deeper diving areas of pools.  At this time, acceptable engineering materials that are more slippery than present pool finishes are not known.   In those areas of a pool where the water depth is shallow enough for a swimmer to stand up, the use of very slippery finishes might reduce the incidence of diving accedents resulting in spinal cord injury, however, it would, in all probability, increase the incidence of drowning.  The shallow areas of pools must be optimized to provide maximum safety to the individual who is just learning to swim or who is an unskilled swimmer.  As the industry pursues engineering changes that increase the degree of safety afforded to a shallow water diver, it is important that the safety of unskilled swimmers who are the predominant users of the shallow area of pools not be compromised.

    It is further observed that a motion arresting mechanism or cushion installed on the bottom of a pool to protect a diver against injury, must not reduce the probability that the head will slip on the bottom.  If such a device interferes with slipping, it will, in all probability, do more harm than good.   In addition, if devices of this type were installed in the shallow areas of pools where the great majority of diving accidents resulting in injury to the cervical spine occur, they would endanger the nonskilled swimmer because they would interfere with his secure footing.

2.2 Warnings

    In the past, there has been no general awareness on the part of the divers, diving coaches, the public, or the swimming pool industry of the potential for serious injury to the cervical spine as a result of diving.  The risks are documented in this study and they are significant.  It is recommended that the National Swimming Pool Foundation uses the means at its disposal to teach and to warn the public that diving without proper caustion and training, whether it be in pools or in the natural environment, involves risk of injury to the cervical spine.

    The posting of additional depth markers or warning signs could well provide a false sense of security. It is doubtful, that had such warnings been posted, they would have influenced the accidents reviewed in the course of the study. As a general rule, it was found that diving accidents in pools occurred in circumstances in which the injured diver had been in the pool many times before and there was little or no uncertainty as to the depth of water or the configurattion of the pool. Therefore, for this reason, no recommendation is made for additional markers or diving prohibition signs at this time. The principal emphasis of the Foundation should be to direct its efforts toward developing a public awareness of the risk, toward defining and curing the root cause of this type of accident. The emphasis should not center on measures that, in all probability, would be ineffective and merely self-protective.

2.3 Training

    It is recommended that the Foundation transmit the findings of this study to those agencies that provide water safety training including but not limited to the Red Cross, YMCA, YWCA, Boy Scouts and Girl Scouts, and other organizations, so that these agencies can jointly, with the Foundation, make the public aware of techniques for avoiding diving injury.

    It is specifically recommended that general prohibitions against diving into shallow water in pools not be adopted. Such a prohibition would remove a training opportunity during the "safe years" below the age of thirteen, and amplify the already much more severe problem during the "dangerous young adult years" of untrained divers diving in the natural aquatic environment.

December 19, 1980

Mr. Lief Zars, Chairman National Swimming Pool Foundation
c/o The Gary Company
302 East Nakoma
San Antonio, Texas 78216

Dear Lief:

Enclosed are four drawings which describe the results of calculations for dives from a one meter (3'-4") and a three meter (10'-0") board. The diver is assumed to have the following characteristics:

                            Height hs                                 6'-0"
                            Weight                                     200 Pounds
                            Vertical Jump                        2'-0"
                            Delay Length                         0.4 h s
                            Drag Coefficient                  1.0
                            Take Off Angle                     150< < 75 0

In these analyses, I have calculated speed as a function of distance traveled underwater assuming that the diver makes no attempt to change direction or ' to slow down following water entry. Using the results of these calculations, I constructed the constant speed contour drawings that you requested. In addition, I am enclosing two additional drawings in which maximum depth contours were constructed under the assumption that the diver steers with a constant turning radius after his head enters the water. I think you will find these last two drawings to be of interest.


The first two drawings show contours of constant speed vs. distance traveled underwater for the one meter and three meter cases respectively, under the assumption that the diver continues in a straight line following water entry. These contours indicate speed when the head is at the indicated depth.


Allowing one foot for the distance from the top of the head to the hands for available stopping distance indicates that the bands would contact the bottom at speeds in the range from 11-13 1/2 feet/second for the proposed APRA one meter pool shape and in the range from 12-14 feet/second for the NSPI Type VIII one meter case. If the diver's motion is to be arrested in one-foot of travel, these speeds require that the diver exert an average stopping force in the range from 376 to 566 pounds in the APHA case and in the range from 447-609 pounds for the NSPI Type VIII case.


With a dive from a three meter board (10'-0") , the hands contact when the diver is traveling with speeds in the range from 13 1/2 to 14 1/2 feet/second for the proposed APHA three meter case and in the range from 14 1/4 to 17 1/2 feet/second for the NSPI Type IX three meter case. The corresponding average stopping forces are in the range from. 566 to 631 in the APRA case and in the range from 631 to 951 for the NSPI Type IX case.


These two constant velocity contour drawings illustrate our earlier conclusion that it is not feasible to rely only on the path length of water to slow a diver to where he can safely use the stopping power of his hands and arms to pretect himself against hitting his head, if he makes no attempt to steer. The force required to arrest motion is unreasonably high, the time available for stopping is short compared to normal reaction times and the required stopping power is in excess of normal human capability.

One would be hard put to justify either the present NSPI or the proposed APRA pool shapes and sizes on the basis of safe bottom contact speeds under the assumption of no steering on the part of the diver. It would be even more difficult to quantify any improvement in diving safety related to reducing contact speed by two to three feet/second when all of the calculated contact speeds are in excess of those that a diver can manage without steering.


I believe that an individual who dives head first into water of limited depth from a deck, platform or diving board must assume a responsibility for steering safely underwater. The fact that there are so few accidents in the millions upon millions of dives that are made every year testifies to the fact that the vast majority of people do,, in fact, steer safely.

Automobiles rely more on their steering ability than they do on their braking ability to maneuver to avoid accidents. Just as highway engineers design roads to accommodate the steering capability of automobiles, I suggest that swimming pool designers have a responsibility to provide diving facilities that accommodate the steering capability of divers. Our earlier experimental observation that very few recreational divers ever touch bottom is evidence that this steering objective is largely met by current designs. It is true that competitive divers often go to the bottom. However, I believe this to result from specific training intent rather than any type of steering constraint.


Consider a diver who dives from a board of a given height and enters the water at varying distances from the tip of the board determined by how steep a dive he makes. Assume further that, at the time that the diver's head enters the water, he steers along a circular path of constant turning radius determined by steering forces generated by the use of his hands, arms and legs as well as by arching his back. The full range of dives from very steep to shallow with a constant turning radius generates a pool shape which is determined by the assumed radius.

If a pool was designed to fit a contour of constant turning radius, a diver steering on a curve with that radius would find himself traveling parallel to the bottom at the extreme of his dive.


Contours of constant turning radius were constructed for dives from a one meter board as shown in Drawing Number 3. In this drawing, it is found that over the range of distance extending from about eight feet to 24 feet from the tip of the board, the present NSPI Type VIII one meter shape and the proposed APHA one meter shape correspond very closely to contours of constant turning radius of 9'-6" and 10'-0" respectively.

It would appear that through the design evolution process, both NSPI and APHA have arrived at a shape that requires constant steering effort on the part of the diver. The open question between these two shapes for the one meter (3'-4") board is whether that steering effort should be based on a 9'-6" turning radius or a 10'-0" turning radius.

At distances of less than eight feet from the one meter board, a diver would have to steer down instead of up in order to contact the bottom, for dives with take-off angles of up to 75 degrees. This is obviously poor diving practice for a normal forward dive. However, it would be a normal requirement for a back dive. It would appear that the pool shape and depth in the area under the board to a horizontal distance of approximately 8'-0" out from the tip of the board should be based on expected underwater trajectories for back dives.


The concept that the design of pool shape and size evolved on the basis of a constant steering requirement independent of the type of dive is not nearly as well established in the case of a three meter (101-0") board as it was in the case of a one meter (3'-4") board. Referring to Drawing Number 4,it is seen that the NSPI Type IX profile is fitted by a contour of constant turning radius of between 10'-0" and 10'-6" over a range of horizontal distances extending from 20 to 32 feet from the tip of the board while the shape varies from a 12'-0" contour to a 10'-6" contour over a range of horizontal distances extending from about eight feet to 20 feet from the tip of the board.

The proposed APHA three meter shape and size is well fitted by a 13'-0" constant turning radius over the range of horizontal distances extending from 20 to 32 feet from the tip of the board. In the range of horizontal distances extending from eight to 20 feet from the tip of the board, the APHA contour varies from a 12-foot turning radius to a 13 foot turning radius.

It is thus observed that while the current NSPI Type IX three meter and proposed APRA three meter contours make essentially the same steering demands on a diver making a very steep dive, the NSPI profile demands a greater steering response (12 foot radius reducing to 10 foot radius) as the diver dives further out in the pool while the proposed APRA three meter demands less steering response as one dives further out in the pool (12 foot radius increasing to 13 foot radius) .

As noted in the discussion of the one meter case, in the three meter case the diver who comes to the bottom in the area under the board out to a distance of eight feet from the tip is either making a very steep dive and steering in the wrong direction or he's making a back dive.


On the basis of this brief look at possible criteria for selecting pool size and shape, I'm of the opinion that the concept of shape and size determined by "steering demand" provides a better rationale for setting pool standards than one based on possible contact speeds. This concept has the advantage that it frankly addresses the fact that practical pools are designed to provide maneuvering room rather than to arrest motion prior to the time that a diver contacts bottom if he-doesn't steer.

It does not appear that any present or proposed pool shape or size can possibly reduce contact speeds to tractable levels. I don't see how one can conclude that adding a foot or two of depth provides greater safety under the condition of no steering if the contact forces are in excess of those that a diver can manage.

I believe that the concept of "steering demand" provides, in theory what has been found in practice - to provide safe pools. The upslope as one proceeds out in the pool from the board appears to closely approximate contours of constant turning radius for the shapes addressed in this report. I think that the concept of specifying pool shape and size on the basis of steering demand is new and that it should prove useful. I don't presently have the data to determine what constitutes reasonable steering ctemand for either front or back dives. However, if in your discussions with APRA, this concept is looked upon with favor, I would like to have an opportunity to develop it further. We have the necessary equipment to make measurements of individual steering capability and have done some preliminary analyses to understand the process.

I trust that these drawings will prove useful to you.

Have a Happy Christmas and a Great New Year


Richard S. Stone


Enclosures: Four



A Report to the
National Swimming Pool Foundation
October 1981

Prepared by
Richard S. Stone
Arthur D. Little, Inc.
Cambridge, Massachusetts  02140


Richard S. Stone

    Experimental Observations
    Theoretical Considerations
        Steering Force
        Drag Force
        Total Force
    Description of the Rating Method
    "Worst Case" Diver
    Air Trajectories
    Underwater Trajectories


    This report suggests a method for rating the match between a diving board of a given height and the design of the pool diving area in terms of its depth and shape. The method is based on a knowledge of the speed and distance a diver can attain at water entry, the angle of water entry, the rate that he slows down underwater and, most importantly, the steering effort required to avoid contact with the bottorn.

    The rating technique based on experimental observation of diver's behavior underwater and on analysis of the forces required for steering. For purposes of illustration, the technique is applied to a number of pool designs suggested by the National Swimming Pool Institute and the American Public Health Association.

    The requirement for underwater steering in diving must be recognized at the outset. Obviously, if a diver dives down and doesn't steer up, he will hit bottom. It is important that all concerned; the pool owner or operator, those responsible for supervision and training and every diver; know what is required to avoid hitting bottom.

    However in diving, being forewarned may not necessarily be forearmed. The accumulating data on diving accidents resulting in serious injury suggests that a large portion of these accidents may occur when divers lose control of their underwater trajectory. If this is the case, forwarning divers on the steering effort required or even deepening pools by a foot or two to reduce the required steering effort may not materially reduce the number of such accidents.

    Two things are needed.  First, divers must know the shape and depth of the area into which they are diving and second, they must be taught how to steer and avoid loss of control over their underwater trajectory.  The rating technique suggested in this report addresses the first need.  In the author's view the second need can only be addressed through a vigorous widespread educational program.


This study shows that it is possible to generate water envelope profiles corresponding to the range of possible trajectories in air and underwater for a "worst case" diver for an assumed constant underwater steering effort. It is suggested that pools equipped with diving boards can be rated in terms of the steering radius of curvature required of a "worst case" diver to avoid contact with the bottom. In this way pool owners and divers can be made aware of the essentially absolute requirement for steering underwater and know what is required to dive safely in a given pool.

It is further shown that in the proposed NSPI designs, the required steering effort is essentially constant, independent of whether the diver makes a very steep dive or dives far out in the pool.

It is found the required turning radius for the APHA designs are one to two feet greater than that for NSPI designs with similar diving board heights. In addition, in the case of the APHA designs, the match between the water envelopes calculated for constant steering effort and the pool shape are not as close as that observed in the case of the NSPI designs. Thus, in a APHA design pool, it requires a different steering effort to avoid contact with the bottom for a steep dive than for a shallow dive.

    The research covered by this report can be summarized as follows:
It has been shown that


    This research shows how and to what extent divers can steer underwater. It provides a method for rating pools equipped with diving boards in terms of the steering effort required to avoid bottom contact. It suggests that pools equipped with boards should be labeled so that pool owners and divers can know what is required to dive safely. It should be emphasized that the calculated turning radius required to avoid bottom contact provides a margin for error since this trajectory brings the diver tangent to the bottom. He might scrape his chest but with this turning radius there is no risk of hitting the top of the head.

    We now know what divers can do, we know what they must do, we can inform owners and users as to the requirement for safe diving. The question remains as to whether or not the divers will make the required steering effort. This can, in my mind, only be addressed through diver education programs.

    The second unresolved question has to do with the development of consensus on what is a reasonable demand on the diver by the pool designer. This research has shown that for low boards, present and proposed designs demand that the diver steer with an underwater radii of 5' to 6'. This appears to be well within the observed capability of our experimental divers.

    Related experiments have shown how a diver can lose control of his underwater trajectory through improper use of the hands and arms. If this happens, the diver ends up headed straight toward the bottom with his hands and arms in a position where they can't protect the head. This type of loss of control is, in the author's mind, probably the principle cause of major injury in diving, but there is little in the way of statistics to prove that this is so. The loss of control happens so rapidly that injured divers have little memory of what happened. It is not clear that increasing the depth of a pool by a foot or two would materially reduce the frequency, of accidents suffered by divers who lose control of their underwater trajectory in this way.


    The objective in the design of a diving facility is to provide an area whose depth, shape and size match the characteristics of the board sc. that the water envelope is sufficiently large to allow a diver a wide margin for error in the performance of his dive -- on the board, in the air and underwater.

    With the recognition that it is not possible to provide engineering designs that will tolerate all errors, it is suggested that pools equipped with different types of diving boards be rated and labeled in accordance with the steering effort required to avoid bottom contact. In this way, pool owners and divers can be informed as to what is required. to assure safe use.

    It is further suggested that in the design of diving facilities, the depth of the area in front of the diving board be configured to require a constant steering effort independent of the type of dive that one might choose to make. In this way the design of the diving area would be consistent in that the same steering effort would be required for steep dives as for a shallower dives.


    Earlier research2 shows that you can't rely only on the distance traveled through water to slow a diver to a low enough speed to chance hitting his head on the bottom without risk of serious injury. As noted above, if one makes a head first dive into water angled toward the bottom at any reasonable depth and doesn't make any effort to change direction, or to slow down, he will go to the bottom and hit at speeds above those that can cause injury to the cervical spine. Depending on speed angle of approach to the bottom and strength, it may or may not be able to avoid injury by using the hands to push off the bottom to slow down and/or to change direction.

    A reasonably athletic six foot tall individual will enter the water at a speed of up to 13 ft/sec in a standing dive from a pool deck, of up to 22 ft/sec from a one meter board and at up to 30 ft/sec from a three meter board. If this diver holds his hands outstretched over his head and extends his body, it is observed that after his head is 2 112 feet underwater he is still traveling at a speed equal to that at the time or head entry into the water. He will then lose about 10% of his remaining speed for each additional foot traveled. Thus, after he has traveled 9 1/2 feet, his speed will be equal to one half his entry speed and after he has traveled 16 1/2 feet, his speed will be halved again. That is about 3 ft/sec for the dive from the side of a pool, 5 ft/sec from the one meter board and 7 1/2 ft/sec from the three meter board.

    Fondation research3 has shown that if a heavy diver hits bottom at a steep enough angle so that the head doesn't slip, sufficient force can be generated to dislocate the cervical spine if one hits at 2 ft/sec.     At 4 ft/sec, sufficient focce will be generated to crush cervical vertebra.    In the three cases above, speeds would have to be     reduced by additional factors of two to four or more before contact speeds would be reduced to below 2 ft/sec. That requires increasing the underwater path length by 7 to 14 feet.     That is, from 16 1/2 feet to 23 1/2 for the dive from the deck and to 30 1/2 feet for the dive from a three meter board. Even this provides little margin for safety,    but it results in a diving area design that is completely

    It's clear from these data that its not feasible to rely only on the distance through water in diving to slow a diver to the point where there is tic risk hitting the head on the bottom with sufficient speed to cause injury. There is a basic requirement that the diver steer underwater to avoid potentially injurious impact with the bottom in any practical pool.


Experimental Observations

    A series of diving experiments were performed at the Swimming Hall of Fame in Fort Lauderdale in which motion pictures were taken of divers underwater trajectory when diving from different heights and making varying efforts to steer underwater. Steering effort ranged from none at all to the maximum that the divers were comfortable with.

    Independent of whether the dive originated from the side of the pool, at deck level, or from a three meter board, in the steeper dives with no steering effort, . the observed underwater trajectories were straight and consistently went to the bottom of an 18 foot deep pool. The diver's speed at the bottom in these dives was such that if they did not protect themselves using their hands to push on -the bottom, their head would have hit bottom with sufficient speed to risk serious injury to the cervical spine.

    In succeeding dives, increasing efforts were made to steer toward the surface by tipping the hands and arms up, by extending the head, arching the back and flexing the knees. In dives in which the diver's attempted to hold their body configuration constant, it was observed that after an initial penetration of the head of approximately 40% of the divers height, the subsequent underwater trajectory of the diver's center-of-gravity was observed to be circular. The diver's body was inclined at a constant angle of attack relative to the trajectory of the center-of-gravity. The head traveled on a radius somewhat less than that of the center-of-gravity while the trailing legs traveled on a circle of somewhat greater radius. A diagram for a dive considered to be typical of those observed is shown in Figure 1.

    In the case illustrated for a dive from a three meter board, after traveling an initial distance of approximately 40% of the divers' height, the head, center-of-gravity and the trailing legs were subsequently observed to travel around circles with three feet, four feet and five feet radii, respectively. Similar trajectories characterized by a delay length followed by a circular path for the head, center-of-gravity, and trailing legs were observed for dives from the pool deck.  In the case of these dives, the delay length might have been somewhat less than those observed for the dives from the three meter board. However, there is insufficient data to establish this distance with high precision.

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    It should be emphasized that these experiments did not determine either the minimum delay length or the minimum turning radius for the divers participating in these experiments. The examples sighted are illustrative of what a reasonably athletic, six foot tall recreational diver can do comfortably. In these experiments, the minimum radii of curvature of the trajectory of the head was observed to be 21-611 for both deck dives and in dives from the three meter board.

Theoretical Considerations

Steering Force

    If a diver with a constant body configuration is to travel on a trajectory of constant radius, it is necessary to provide a steering force acting through the diver's center-of-gravity perpendicular to his instantaneous direction of motion as illustrated in the force diagram shown in Figure 2. In order to maintain a circular path, it is necessary for the steering force to be equal to the diver's mass times his centrifugal acceleration. That is

Fs(t) = W/G x S2(t)/Rcg


Fs(t)      is the steering force
W          is the diver's weight in air
h           is the value of local gravity
S2(t)    is the speed of the diver's center-of-gravity
Rcg     is the rakius of the trajectory of the center-of-gravity

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Drag Force

    In addition to the steering force action radially, there is a drag force acting tangent to the circular path shown as FD in Figures 2.  If one plots the speed of the diver's center-of-gravity vs. the distance traveled underwater, a logarithmic slowing down characteristic is obtained.  An example is shown in Figure 3 in which a six foot tall diver dove from a three meter board and following water entry he was observed to steer around a path with a four foot radius.   The logarithmic slowing down in shich one loses a constant fraction of their speed foloowing an initial dely length can be expressed mathematically in the form

S(t) = S(0)e                                          


S(t)     is the speed of the diver's center-of-gravity
S(0)    is the speed at the time the diver's head enters the water
CD     is the effective drag coefficient for the diver's body configuration
hs       is the diver's height
S(t)    is the distance traveled from the point of head entry
So      is the diver's delay length taken at 40% of the diver's height.

In Figure 3, it is observed that after the hydrodynamic forces acting on the diver are fully developed, the diver loses half his speed for every additional 2.5 feet traveled.  From Equation (2) this rate of loss of speed corresponds to an effective drag coefficient of 2.4.  This drag coefficient corresponds closely to measured coefficients for six foot tall divers making flat hand entries with no steering effort.

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The drag force acting on the diver can be obtained by differentiating Equation (2) and multiplying by his mass.  This results in an expression for the drag force of the form

FD(t) = W/g x CD/2hs x S2(t)


The total force acting on the diver can be written as the vector sum of the drag force and the steering force.  Since these forces act at right angles, it follows that

F(t) = {Fs2(t) + Fd2(t)}1/2

Substituting for FD and FS and dividig by the diver's weight, yields an expression for the total G force acting on a diver as a function of his speed and the radius of his underwater trajectory in the form

G = CDS2(t)/2ghs x {1+(2hs/CDRcg)2}1/2

    This expression for the G force acting on a diver has been plotted as a function of the speed and radius of curvature of the underwater trafectory.  Assuming a six foot tall diver holding a body configuration which yields an effective drag coefficient of 2.4.  The results of this calculation are shown in Figure 4.  Also shown in this figure is the calculated range of water entry speeds for divers diving from a deck six inches above water and from diving boards ranging in height from 20 inches to three meters above the surface of the water.  The range of entry speeds is calculated assuming that the diver has sufficient strength in his legs to jump vertically to a height of between one and two feet.

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    From this figure, it is possible to obtain the G force acting on a hypothetical diver from a knowledge of his speed and steering effort.   For instance, assume that a diver dives from a three meter board, and enters the water with a speed of 20 ft/sec, and makes no steereing effort (infinite radius of curvature) as indicated at pooint A in the figure.  With a flat hand entry, when the diver's head is approximately 2 1/2 feet underwater he will be subjected to a maximum force of 4.9 G.

    It shoud be boted that this force level persists for a very short time.  After the diver has traveled an additional 2 1/2 feet in approximately 0.16 seconds, his speed will be cut in half to 14 ft/sec and the G force will be reduced by a factor of four to 1.2 as shown by point B in the figure.

    If this diver makes the same dive but now steers so that his center-of-gravity follows a three foot radius trajectory underwater, after the initial 2 1/2 feet of travel, the initial G force is increased 9.5 G as shown at point A1 in the figure.  Again, the diver's speed is reduced to about 14 ft/sec after traveling an additional 3 1/2 feet in approximately 0.16 seconds.  At this time the G force on the diver is 2.6 G as indicated at point B1 in the figure.

    Data on the acceleration tolerance4 obtained by NASA indicates that in this range of time duratin, human subjects are uninjured or undebilitated by force sevels of up to 30 to 40 G.  In experimental studies, individuals are willing to voluntarily subject themselves to these higher levels of force.   One concludes that even in diving from a three meter board and making a steering effort to direct the center-of-gravity around a circle as small as three feet in radius, the force levels experienced are well below human tolerance with a wide safety margin.


    Description of the Rating Method

    We now have the scientific data necessary to rate pools equipped with diving boards in terms of the steering effort required of the "worst case" individual to avoid contact with the bottom over the full range of possible forward dives.

    From our knowledge of the possible trajectories in air a "worst case" individual can attain, its possible to predict how far this individual can project himself out from the tip of the board over the range of possible dives.  In addition, this knowledge makes it possible to predict the divers speed and direction of motion at the time his head enters the water.

    Give the range of possible entry positions, speeds and angles combined with the new knowledge gained in this research on how divers can steer underwater, its possible to predict the underwater trajectory of the "worst case" diver for a giben steering effort.  Combining the range of possible air trajectories with the underwater trajectory one generates a water envelope for this diver for a given steering effort.  As long as this diver makes a steering effort equal to or greater than the indicated effort, he will remain inside the calculated envelope.   The calculated water envelope can be overlaid on suggested pool designs to illustrate which dives require the most steering effort and which require the least.

    It is suggested that an optimum design would be one in which all possible dives required the same steering effort.  In this way, the diver would not be subjected to different steering demands for different types of dives, there would be no surprises built into the design.  The pool designer would be optimizing the design fo maximum effectiveness.  For example, he would not make the area immediately under the board excessively deep if the limiting dive were one that lead to one that was tangent to the bottom further out in the pool on the upslope.

    By overlaying a suggested pool design with a calculated curve-of-maximum-depth for the "worst case" diver, it is possible to rate the pool in terms of the required steering effort.  Specifically this rating would be the minimum radius of curvature that the "worst case" individual would have to steer to avoid bottom contact.

    Prior to illustrating the use of this rating method, it is necessary to define our "worst case" diver and understand the limits on his trajectory in air an underwater.

    "Worst Case" Diver

    A tall athletic individual can project himself further out in a pool, and attain higher water entry speeds than shorter less athletic individuals.  In the water, a taller individual has a greater delay length following water entry and he must generate proportionately higher steering forces tha a shorter individual to steer a trajectory of given radius.  In addition, a tall individual goes faster further underwater tha a short individual.  To the extent that height and weight are correlated, the taller heavier individual will be subjected to greater force if he fails to steer and impacts the bottom.  Thus, in all regards, the tall athletic individual represents a "worst case" for diving safety.

    In our "worst case" calculations, we will assume a "worst case" diver who is six feet tall and has sufficient leg strength to jump vertically two feet.

    A springboard is an energy storage device that at best can, at the time a diver leaves the board, return the energy that has previously been stored in the board by the diver in his approach. It was found that a diver who had sufficient leg strength to jump vertically a distance of two feet would leave the board with a speed corresponding to a vertical jump of four feet. Thus, he takes off with essentially all of the energy stored in the board associated with the hurdle jump plus that of his spring jump.

    In addition to take off speed, the diver has a wide choice in his take off angle. This can range from a very flat dive that projects him far out into the pool to a very nearly vertical dive which brings him into the water close to the board. Experimental observations indicate that divers typically leave the board with take off angles in the range from 15 to 75 degrees. However, to assure that the full range possibilities are covered, in the following calculations, it will be assumed that the diver can take off at angles of up to vertical (90 degrees.)

    Once the diver is in the air, the only effective force is gravity acting vertically downward. Physics dictates that no matter how the diver twists, turns and folds his body the air trajectory of his center-of-gravity is completely determined by gravity, his take off speed and take off angle. His horizontal speed remains constant while his vertical speed decreases linearly with time, so that he goes up. stops and then starts to come down with increasing speed as he moves out from the tip of the board. These constraints on his speed dictate that his center-of-gravity follow the same type of parabolic path that a cannon-ball or baseball follows.

    To make a clean water entry, its necessary for the diver's body axis to be closely aligned with his direction of motion. Since we
know where the divers center-of-gravity is throughout the air trajecory, knowing the diver's height, we can calculate where the diver's head will enter the water, as well as how fast and in what direction he will be traveling at that time.

    The equations that predict the motion of the center-of-gravity in air for our six foot tall diver taking off with a speed corresponding to twice the energy associated with a vertical jump capability have been programmed for a computer.  Given the height of the board and the take off angle, this program calculates thed diver's trajectory in air and yields the position at which the head enters the water, his speed and direction of motion.

    The range of possible air trajectories for our "worst case" diver are plotted in diagrams for seven different suggested pool designs.

    Underwater Trajectories

On the basis of the experimental observations and theortical analysis described in the preceeding section, on concludes that a diver can generate the hydrodynamic forces to steer his center-of-gravity around a four foot radius without undue effort or discomfort.  It is further observed that the underwater trajectory doesn't become circular until the hydrodynamic forces on the body are fully developed at about the point where the head has penetrated the water to a distance of about 40% of the diver's height.

    The underwater trajectory for a six foot tall diver is initially a straight line for approximately two and one half feet from the point of entry inclined at the diver's angle of entry into the water.  Subsequently, if the diver holds a fixed body configuration to yield a constant steering effort his underwater trajectory will be a circle of fixed radius with the radius determined by the diver's stature and body configuration.  Most improtantly, it appears that meither the initial straight line delay length nor the radius of the circular trajectory are dependent on the diver's speed.  That is independent of the speed of entry, with a fixed steering effort, the diver will folow the same underwater trajectory.

    In the following section on application of the rating method, the range of possible trajectories in air have been combined with the underwater trajectories associated with a given steering effort.  These composite trajectories yield a steering envelope for the "worst case" diver that are overlaid on the various pool designs to determine


    Seven different suggested pool designs were studied.   Four of these were proposed NSPI designs with diving board heights ranging from 20" to one meter and three APHA designs with diving board heights of 24", one meter and three meters.

    The range of possible air trajectories for the six foot tall "worst case" diver were calculated assuming a two foot vertical jump capability, to obtain the position of water entry and the direction of motion at entry.   The trajectory in air was joined to an underwater trajectory composed of a 2'-5" straight line segment continuing at the water entry angle followed by a circular trajectory of constant radius corresponding to a fixed steering effort.  In each case, the radius was adjusted to best match the calculated steerin g envelope to the shape of the particular pool.

    The results obtained for the four proposed NSPI designs are illustrated in Figures 5 through 8, while those obtained for the APHA designs are shown in Figures 9 through 11.  The results in terms of the turning radius required and the limiting type of dive for the "worst case" diver are summarized in Table 1.

    Table 1 shows that for the NSPI Type II and III type pools, the "worst case" diver must steer an underwater trajectory with a five foot radius to avoid bottom contact.  The type IV pool requires a radius of 5'-8" while the Type V pool with one meter board requires a turning radius of 6'-0".

    The suggested APHA designs are seen to require a turning radius that is about one to two feet greater than that required for the NSPI design with a corresponding board height.

    It is also observed that in the NSPI designs, the calculated envelopes for constant steering effort corresond very closely to the shape of the pool.  As a result, there is no limiting dive ans all possible forward dives into one of these pools requires essentially the same steering effort.  In the APHA low board designs, a greater steering effort is required for steep dives than for dives further out in the pool.  In the APHA three meter case, there is a reasonable match between the calculated water envelpe for a 9'-2" turning radius far out in the pool while the steering radius is increased to almost 10' close into the board.  Thus the further out in the pool one dives, the greater the required steering effort.

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Turning Radius
Limiting Dive
Steep Shallow
II 1/2 Meter (20") 7'-6" 5'-0"    
III 2/3 Meter (26") 8'-0" 5'-0"    
IV 30" 8'-6" 5'-8"    
V One Meter (40") 9'-0" 6'-0"    
Deck Level 24" 8'-6" 6--0" X  
  One Meter(40" 10'-0" 7'-8" X  
  Three Meter (10') 12'-0" 9'-2"   X


  1. How Diving Accidents Cause Quadriplegia, Richard S. Stone and John D. States, to be published.

  2. "Diving Safety in Swimmin Pools," A report to the National Swimming Pool Foundation by Richard S. Stone, May 15, 1980.

  3. loc cit.

  4. "Bioastronautics Data Book," Paul Webb, M.D., Editor, Scientific and Technical Information Division, National Aeronautics and Space Administration, Washington, D.C., 1964.


ADL 5 Attachment

March 17, 1982

Mr. Larry E. Paulick, P.E.
National Swimming Pool Institute
2000 K Street, N.W.
Washington, KC  20006

Dear Larry:

Enclosed are the new drawings on the proposed types of pools that are designed to be equipped with diving boards.  I have carried out a worst case analysis to determine whether the individual types provide a large enough water envelope to allow a diver to steer comfortably and to avoid bottom contact.

The analyses conseder a worst case diver 6'-0" tall with sufficient leg strength to jump vertically 2'-0".  The diving trajectories considered include a verticle dive right off the top of the board to a dive that projects the diver as far out in the pool as possible.  It is assumed that, after entering the water, the diver continues in a straight line for a distance equal to 40% of the height without slowing down.  The diver is then assumed to make a steering effort through the use of his hands and arms, lifting his head and arching his back and/or cocking his knees, which generates an initial 3G steering force.  I have established that the assumed initial steering forceis weel within the comfortable capability of recreational divers from the research that I've carried out for NSPF on underwater steering.

If, subsequently, the body configuration is held constant, the diver will travel on a circular path of constant radius.  These circular contours with radii corresponding to an initial steering force of 3G have been constructed for each dive.   A Dotted contour or envelope has been plotted to show the closest point-of-approach to the bottom for the full range of possible front dives on each drawing.

I find that the worst case diver will clear the bottom of the pool by between 9" and 1'-4" under the assumption of the 2'-5" delay length, ine initial steering force of 3G and the particular type of pool being considered.

I find further that the designs of the individual types of pools are internally consistent in that they provide approximately the same clearance margin for very steep and very long dives, with a slightly greater margin for dives with the normally expected 45-60 degrees takeoff angle from a spring board. As a result, I find that there are no surprises in the proposed designs. Independent of whether one makes a very steep dive, a normal dive, or a dive far out in the pool, it is necessary for the diver to make an essentially constant steering effort

I do have two reservations about these analyses that perhaps should be noted in your standards.

The first of these is the fact that the analyses illustrate dramatically the absolute requirment for steering if one is going to dive confortably and safely In a pool designed to the NISPI standards. I believe that it is of the utmost importance that every effort be made to make the pool industry, pool owners, and divers aware of this. I come back to my statement: IF YOU DIVE DOWN YOU MUST STEER UP.

My second reservation has to do with back diving. Residential pools equipped with springboards are not to be confused with competitive diving facilities and under no circumstances should one attempt to do a back dive into a residential pool. In a competitive diving facility, diving boards are provided with sufficient overhang from the plummet to allow one to safely and comfortably complete their underwater trajectory in a back dive as trajectory curls back under the board. This is not the case in a residential pool, and it should, in my opinion, be noted in the standards.

I trust that these data will illustrate why I think that the proposed individual pool designs are internally consistent and why I believe that the designs provide sufficient water envelopes for divers that will steer correctly to dive with safety and comfort. .

If you have any questions, don't hesitate to give me a call.


Richard S. Stone

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