Fun With Math

Today on my 8 cycling loops of the Kemah Bridge, I thought I'd try and estimate the elevation of the bridge. I have looked for it online, but have yet to find it. On the other hand, the statistics for the newer and larger Fred Hartman Bridge can be found easily on a search. The deck of that bridge rises to 178 feet, which makes it a more uplifting experience than Kemah. I may move my bridge repeats there.

Fortunately, the bridge spans two roads, one on each side, and there is an elevation marked on the bridge for trucks. On the Seabrook side, the span is 17 feet and 5 inches. On the Kemah side, the span is 19 feet and 6 inches.

Using those two markers, and their position on the bridge, I guessed the bridge rises about 55 feet. At this point, I decided to bring some mathematics into the estimation. On the next two loops using my bike's distance calculator, I measured the distance from the points where I knew the elevation to the top of the bridge.

The distance from the 17'5" point to the top is 0.27 miles. On the other side, the distance from the 19'6" point to the top is 0.25 miles. At this point, one has to make a big assumption. Let's assume that the slope on each side of the bridge is the mirror image of each other. By difference, one can then say that the bridge rises 2 feet and 1 inch for each 0.02 miles. Unfortunately, we really need a third decimal place for this analysis, so lacking it will introduce some error.

OK, now another gross assumption is necessary. Let's assume the average slope of the bridge from the point of measurement to the top is exactly the same as the average slope over the 2'1" that we measured by difference. Ouch, this will definitely introduce more error. The slope does seem to increase some for 0.16 miles when it then starts to level out to the summit for 0.09 miles. But there is no reason why the slopes would be the same as my assumption suggests.

In any rate, one can estimate the height of the bridge as follows:

19'6" plus (2'1" times 0.25 divided by 0.02) plus 3' (for the difference between the bridge deck and underneath where the span clearance was measured).

This equals 48 feet and 6.5 inches. Most likely the slopes are not equivalent and the actual span is slightly higher. I will go with 50' until I know better.

This is what happens to ones brain on repetitive bridge loops. When I am doing 12 loops I'll bring out the trigonometry. Oh the joys of nerddom.

5k run at Seabrook followed by 23.3 miles ride including the fun with math loops.