Tracking Model Rockets

 

Introduction

Tracking model rocket altitudes is not a trivial endeavor.  Several different methods and techniques are available to aid one in determining the altitude of a model rocket.  These techniques include trigonometry, the use of electronic altimeters or mechanical altimeters, or guessing.  Unfortunately, these all have specific, inherent shortcomings.

In the fall of 1999 a engineering team consisting of two seniors were assigned the dubious task of evaluating several of the tracking methods/techniques, and making a determination as to which was the most effective for students participating in rocket design competitions.  Competitions historically had been held in ME design classes such as ME 223/323 and high school summer science camps such as JEMS.  The engineering team determined that the use of a trigonometry based visual tracking system was the most cost effective and accurate.  

The primary component of the trigonometry based visual tracking system is a angle measuring device loosely based upon a civil engineering theodolite (seen below).  

Typical civil engineering theodolite

 

Theodolite 

The theodolite has the ability to measure two angles, a vertical angle and a horizontal angle.  By coupling the use of two theodolites with their ability to measure two angles, a person is able to determine the exact point in space where the rocket is located.  This is important because a rocket never reaches its maximum altitude, or apogee, directly over the launch pad.  Wind may blow the rocket off course or poor construction may direct the rocket to the side.  Actually the theodolites provide too much information, 4 angles, or four different measurements, one more than the 3-dimensional space in which we currently live.  We can, however, use the extra information to determine how accurate the two stations measured the altitude with respect to each other.  

Math Model

Here is the math model that is used to calculate height using the theodolites.

 

Variables:

A=Horizontal angle from station #1 [°]
b=Distance between station 1 and station 2
C=Horizontal angle from station #2 [°]
D=Vertical angle from station #1 [°]
E=Vertical angle from station #2 [°]

 

 

Altitude 1 and Altitude 2 are averaged together.  This is done with the hope that any errors induced by the user of the equipment will be cancelled out.  If there is more than a 10% difference between Altitude 1 and 2 then the data should be thrown out.  The difference indicates the accuracy of the users of the two stations at pin pointing the rocket at apogee.  Which is much more difficult than it sounds.     

Equipment

Currently the UofI Mechanical Engineering Department has two sets of theodolites for use during rocket competitions.  One set (see fig.1) was fabricated in the fall of 1999 by the engineering team assigned to the project.  This prototype set was constructed mainly of wood and household items to prove the viability of the concept.

fig.1  1st Prototype of the altitude tracking theodolites

Once the concept was adopted, a second set was constructed of aluminum, during the summer of 2000 (see fig. 2).  The second set of aluminum is vastly superior to the first set in accuracy, simplicity, ruggedness and ease of use.  This is primarily due to the introduction of laser sights for visually attaining and marking the path of the moving rockets.  

fig. 2  Second prototype constructed of aluminum.  Note the laser optical site mounted on top.

 

Procedure for Tracking Rockets

Setting up the Theodolites

The most important factor for accurate tracking of rockets depends upon the planning and work done before the actual launch. An accurate measurement of the baseline between the two stations (b) must be taken.  Also, the baseline must be at least twice the length of the estimated height of apogee.  Positioning of the tracking stations is important also.  Both stations must be able to see the launch pad, each other, and the people running the launch at all times.  Any obstructions will hamper the trackers measurements and could pose safety issues.  

Once locations for the theodolites have been determined the theodolites can be set up.  This is relatively simple if the person setting them up has had past experience.  If not, here is a short tutorial. 

  1. Assemble Theodolite
  2. Extend tripod Legs to a height comfortable for the user.
  3. Place tripod with the horizontal protractor's zero aimed towards the other station (this will help you zero the station in sequence #7).
  4. Level the tripod using the bubble level built into the top of the tripod.
  5. Uncap laser sight and turn sight on using the top mounted dial.
  6. Look through the sight and place the laser on the other station.
  7. Bend the pointers to 0° on both the vertical and horizontal protractors.
  8. You are now ready to track.

Tracking

Here is what will happen during a model rocket launch.

  1. The Range safety officer at the launch site will Ok the team to launch.
  2. Two team members will have walkie talkies.
  3. One of those team members will be counting down over the walkie talkie and actually launching the rocket.  The other will be calling mark over the walkie talkie indicating apogee for their rocket. 
  4. The team member launching, prior to launching will check with both tracking stations to verify that they are ready. 
  5. A count down will ensue, then launch. 
  6. Follow the rocket until the other team member calls "mark", at this point stop following the rocket and read and record the angles from the protractors.  The data can be inserted into a calculator (HP 48G program) or spreadsheet to calculate the altitude.