January 03, 2004

How high did that rocket go?

Here's a simple and inexpensive way to get a fair estimate. There are three diagrams, so expand the extended entry to read the surprisingly easy method we use.

You actually only need a couple things to figure out the altitude of your flights. A theodolite, a tangent table, and a pencil. For reasonably accurate readings, you can make the simple theodolite shown in figure 1. It's basically a 1"x2" piece of wood, 2 foot long, with a plastic protractor screwed to the side. Add a couple finishing nails to sight along, a string with a fishing weight at the end to indicate the angle, and you're set.

figure 1

The tangent table can be found in any trigonometry textbook. Use the one shown in figure 2, or find one to your liking, they're all the same.

figure 2

Still with me? Good, believe me, this is simple. In fact, this explanation takes longer than the process.

Figure 3 shows the basic concept of determining altitude:

figure 3

The 'tracker' takes the theodolite and stands a known distance from the launch pad. In the diagram, it's where the black and blue lines meet. This distance is the baseline, and the farther the better (as long as you can see the rockets from there). Our usual launch area is a football field, so our tracker is usually 300 feet (100 yards) away from the pad. The tracker on one goal line, the launch pad on the opposite goal line.
When the rocket launches, the tracker follows the rocket with the theodolite, sighting it like a rifle, until the rocket reaches apogee (it's highest point). The angle is read (where the string marks it on the protractor), and this angle is written down.
Time for some simple math. The formula is on the diagram. Look up the tangent for the angle on the table, multiply that number by the baseline, and that is the altitude in feet. Simple!!!

An example: baseline is 300 feet. measured angle is 40 degrees. The tangent for 40 degrees is .839, so 300 * .839 = 251.7 feet.

This is only one method, there are many others. But this one is cheap, simple, and accurate enough for our purposes. You can find more information about altitude tracking in the Handbook of Model Rocketry, by G. Harry Stine.

Accuracy can be improved by using two trackers placed at 90 degree angles to each other to compensate for rockets that don't fly perfectly vertical. This is the usual method used at altitude contests. We don't bother when we're flying for fun. Truth be told, we seldom worry about altitude anyway, we just guesstimate using the good ol' Mark I eyeball.

Posted by Ted at January 3, 2004 09:45 AM | TrackBack

Mark I Eyeball only has three measurements, tho: High, Really High, and Hey, God! Little help?

Heh. OK, that's my lame attempt at rocket humour. And I haven't even taken any cold medicine!

Posted by: Victor at January 3, 2004 12:29 PM

Dang, I thought I invented that device!
After your post about Air Munuvia's maiden voyage I wondered how you could determine how high it went. "Easy," I thought, "just measure the vertical side of the right triangle by looking along it's hypontenuse from a known length of the horizontal side!" (I never got around to writing up a table, though.)
This is as disappointing as the time when I was in K-mart, aged 9, and discovered that my battery-heated socks idea had already been invented.

Posted by: Tuning Spork at January 3, 2004 07:04 PM

Also, that system is accurate only if the rocket climbs perfectly vertically. It would be a good idea (if you really want an accurate measurement in the case of a competition, say) to have someone else with a perpendicular view to measure the angle from the launchpad to the rocket at apogee.
If the rocket curves toward the tracker then the reading with show that the rocket had reached higher altitude than it actually reached; and it curves away from the tracker then the reading would understate the true altitude.

Posted by: Tuning Spork at January 3, 2004 07:15 PM

psst... Spork... last paragraph. ;)

Posted by: Ted at January 3, 2004 07:42 PM

D'oh! I guess I stopped reading too soon. :)

Posted by: Tuning Spork at January 3, 2004 11:00 PM

Easiest way to tell how high a rocket went is to launch it indoors.


"About eight foot six, wouldn't you say?"

Posted by: Pixy Misa at January 4, 2004 08:09 PM
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