DIVING GEOMETRY
4:1 UPSLOPE


LEIF ZARS

7/29/99

OVERVIEW

All of this work is based on Dr. Stone's work in the field of Diving Geometry.

His reports have been studied carefully and his theories embraced.

His work stated that basically the NSPI diving hopper geometries were in substantial compliance with his research and that they provided a safe environment for diving from a designated location (Point A) and specific equipment types he had evaluated. I fully support his conclusions.

In the past 20 years or so I have seen numerous changes in our society and in our courts. A greater emphasis has been placed on providing "more than adequate" protection for the consumer. It is in this light that the attached study has been carried out.

THE BASIC APPROACH

All diving equipment should be considered on the basis of its ability to multiply the diver's energy (or provide energy from outside sources). Leaving energy from outside sources out of this discussion, we can concentrate on the equipment itself.

Dr. Stone created a graph in which lie related this energy (as a spring constant) to -the equivalent fall height. How much higher than the starting height could a diver propel himself via the mechanics of the board. This height was stated as the "fall height". I start with this graph curve.

To simplify its use I converted the graph into a table that directly shows the spring constant and its related fall height in Ft.

Now to determine the total dive energy into the water we must consider the height of the diving equipment take off point above the water.

To arrive at this total energy it is it simple matter to add together the fall height of the board (or diving equipment) in Ft. with the height of the take off point in Ft. above the water. This combined height energy then easily converts into free fall velocity. The higher you fall from, the faster you enter the water. It is this water entry velocity that I shall use to determine the quantity of water required to adequately protect the diver.

The following table (3 pages) directly translates combined height in feet to water entry velocity. For example, 3.22 feet in total height will result in a water entry velocity of 14.39 feet per second. No other calculations are required.

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THE SLOWING EFFECT OF THE WATER

Dr. Stone reported that it would take up to 23 feet of water depth to adequately protect a diver who did nothing but hold a straight arrow dive approach from impacting the bottom at a dangerous velocity.

He further stated that in tests he could easily perform a 3G steer up maneuver.

In his work he used a 2' steering radius (which is very similar to a 2G steering effort) to depict the underwater trajectories of the center of gravity of a diver.

He helped coin - the phrase "Steer Up" when, diving. He further stated that NSPI's
diving geometry conformed well with a moderate steer up effort.

It is my thought that we as an industry may well focus on providing a somewhat greater factor of safety for the diver. I feel that the societal changes of the last 20 years have brought us to this point. I do not just feel that this something we should do, but that this something that we must do. And I feel that as the leader for the technical advance and well being of the Industry the National Spa and Pool Institute has the obligation to provide Standards in keeping with the times for its members.

To this end I have used a very conservative 1G underwater steering effort on the part of the diver in arriving at some underwater curves depicting the diver's path.

To these sets of curves I have added an optional line depicting a further 6" clearance factor of safety if such is desired. That is something that an informed committee can decide.

Let me further state the degree of conservatism embodied in a 1G steering effort. Dr. Milton Gabrielsen has stated on many occasions that diving from the side of a pool into 5 feet of water is an acceptable and safe dive. Actually, when diving rather steeply from the side of a pool into 5 feet of water one can encounter the bottom as shown in the attached material.

Further, when diving into a FINA 3 Meter diving hopper from a 3 meter tower one can again go beyond the FINA geometry if one uses only a 1G recovery effort. This is also shown in the attached material.

Also is attached a comparison of 3G, 2G and 1G steering efforts. 1G is really conservative in my opinion and as such was used in preparing this report.

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CALCULATIONS

Calculations were made in accordance with the research of Dr. Stone and the basic principles of physics and mathematics. The format follows that discussed in my previous paper entitled "Diving Geometry Handbook" dated 3/8/98.

As an example of one of these calculations I am attaching 4 sheets showing my typical calculations along with one sheet showing the series of underwater curves generated therefrom. This work happens to be for the 16.50 FPS water entry velocity, This work is then used to provide a series of eight underwater trajectory curves representing dive angles of 85, 80, 75, 70, 60, 50, 40, and 30 degrees.

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WATER ENTRY VELOCITY RANGES

In as much as I am using the basic criteria of water entry velocity as the means to evaluate diving equipment and mounting combinations, I felt it best to endeavor to categorize these into usable segments. This has been done on the following page.

This shows numerous diving board and mounting conditions along with diving directly from a pool edge or "diving rock" up to 24 inches in height. Each is arranged in accordance with the resultant water entry velocity generated by the activity,

Looking at this, most typical combinations fall into anticipated categories. For example, 6-foot boards generally fall below 16.5 FPS. Eight-foot boards somewhere between 16.5 and 18.0 FPS. The 10-foot board combinations generally run between 18.0 and 20.0 FPS. Twelve-foot boards start around 20.0 and go to 22.0 FPS with the exception of 12-foot boards mounted with narrow fulcrum setting of 59 inches and a height above the water of 40 inches.

Beyond this would be the 1 and 3 meter boards which it is my understanding that we have decided not to bring into our tables any longer - turning this over to FINA.

Categories were selected according to the above: 6', 8', 10', and 12' boards with their resultant entry velocity categories.

The NSPI tables were then consulted for their suggested water envelopes for each general category. This is shown on the page following - both public and residential. I see no practical way to differentiate between these two categories in as much as identical boards are used in both environments. To modify one group without consideration of the other would perpetuate the present confusion wherein a Type 6 pool hopper is smaller than a Type 5, yet a Type 3 is larger than a type 2, and a Type 4 is basically the same as a Type 6.

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GENERAL COMPARISONS

BOARD Height NSPI Res

Requires

NSPI Public

Requires

Velocity

Range

Velocity

Envelope

6' Board   Type I   16-16.5 16.5
8' Board   Type II   17.7-18 18
10' Board 26" Max Type III Type VI 18.5-19.1 20
10' Board 30" Max Type IV   19.7-19.9 20
12' Board   Type V Type VII 20.5-21.9 22

RESULTANT UNDERWATER SECTIONS

First, the series of curves were plotted. One for 16.5 FPS, 18.0, 20.0, and 22.0 FPS.

These were then underlined on their deepest penetrations into the water envelope. It was found that in all cases this underlining represented very closely a 4:1 sloped line. This line was firmed up as a red line on the following 4 pages. In addition to this, the outlines of each- was concluded by more or less following the previous NSPI geometry on both ends.

In addition, a green line was added 6" below the red line showing the effect of an additional 6" of clearance. This green line was not included in the ends of the curves in as much as there appears no history to indicate a need to provide an additional- factor of safety for the ends of the water envelope,

Following these curves are two depicting the general uniformity of the red and green outlines.

This is followed by a series of 4 curves showing the general agreement of the 4:1 upslope with each set of 1G steering curves.

The next six curves show basically the same thing but with. the corresponding NSPI geometry for the various pool types added. The reason there are six curves is that both the Residential and the Public pool standards are represented. It should be kept in mind that a 1G steering effort is extremely conservative and as such shows up somewhat dramatically in some of these plots.

Finally is the usual question: Where does all of this fit with Dr. Gabrielsen's proposed diving envelope? The blue line on the final curve plot represents his profile for a 12'board. This is superimposed on the 22.0 FPS curve used in this report for a 12-foot board - with limitations.

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DIMENSIONS

The following 4 pages are fundamentally the same as earlier sections but with dimension points brought to scaling points and dimensions added.

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CONCLUSIONS

It has been stated that "If we change now we will be admitting that all we have done in the past is defective and dangerous".

To this end 1 have consulted the advice of an attorney who provided the attached copy of the Federal Rules of Evidence that clearly state: "When after an event, measures are taken which, if taken previously, would have made the event less likely to occur, evidence of the subsequent measures is not admissible to prove negligence or culpable conduct in connection with the event."

 

 FEDERAL RULES OF EVIDENCE

FRE 407.  SUBSEQUENT REMEDIAL MEASURES

"When, after and event, measures are taken which, if taken previously, would have made the event less likely to occur, evidence of the subsequent measures is not admissible to prove negligence or culpable conduct in connection with the event.  This rule does not require the exclusion of evidence of subsequent measures when offered for another purpose, such as proving ownership, control, or feasibility of precautionary measures, if controverted, or impeachment."