Measuring Altitudes

This week we have a look at 4 different ways to measure altitude of a water rocket. We tested all of these techniques on each launch to compare how accurate they are and then we look at the advantages and disadvantages of each.

Technique		Description
Inclinometer		An inclinometer is used to measure the elevation angle of the rocket at apogee from a known distance away from the launch pad. Then using a little trigonometry we can estimate the rocket's altitude.
Ground Photography		This technique involves setting up a fixed video camera a known distance away from the launch pad and filming the entire flight. You can then use a video frame with the rocket at apogee to work out the altitude using a calibration image.
Aerial Photography		This involves placing a small camera on board the rocket and filming the flight looking down. You then select a video frame at or near apogee that has a view of a known size object or feature on the ground. Again using a calibration image you can work out the distance from that object or feature. If that object is directly below the rocket you can work out the altitude.
Altimeter		This technique involves placing an altimeter on board the rocket and measuring the altitude directly. These typically rely on barometric pressure sensors, GPS, or accelerometers to derived the altitude. .

Video

Experiment Setup

Inclinometer

We made the inclinometer from a couple of spare aluminium sections we had on hand. The pivot point was made with a screw and a lock nut. We put a piece of felt between the arm and the base and tightened the lock nut until there was sufficient friction to keep the arm in the set position while still allowing it to easily move. This way you could track the rocket to apogee and then at apogee you would just leave the arm in place so you could record the reading from the side.

We used two different angle measuring devices. We used the classic hanging weight on the end of a thread and a protractor. We also mounted an iPod on top of the arm and used a free App that uses the internal accelerometers to measure the angle. The protractor and thread is good for about 0.5 degree accuracy while the iPod was down to about 0.1 degrees. Most smart phones today can perform the same function.

The whole inclinometer could also be pivoted about the vertical axis so the rocket could be tracked laterally away from the launch pad.

We would always take two readings. One with the inclinometer pointing at the nose of the rocket on the pad as that was about the same height as the inclinometer was above ground. The second reading was then recorded at apogee. The difference between these angles was used in the calculation.

iPod/Smart-Phone inclinometer

Inclinometer App

Classic  inclinometer

Looking down the sight

To work out the altitude we use the following formula:

h = tan(θ) * d where: h is the altitude, θ is the angle of elevation d is the distance from the launch pad.

Ground Photography

The ground camera used in the experiment was the GoPro Hero 3 Black Edition. We set the recording format to 2.7K video with a wide setting. We chose the higher resolution format so it was easier to locate the rocket in the sky and with better precision. The camera was set up on a tripod and angled upwards at around 45 degrees. We also rotated the camera to portrait mode so we could get the most pixels vertically. This would give us enough coverage with the launcher in view near the bottom of the frame and more than 90 degrees above the camera to make sure we caught the apogee of the flight. We located the camera at the same distance from the rocket as the inclinometer. (42.5m)

To get the calibration image, we placed the camera at the same angle, and 42.5cm away from a vertical wall. This would give us a 100:1 scale factor. We then placed markings up the wall and took an image with the camera with the same video settings.

Camera Set up on tripod

Calibration image setup

Calibration image

Aerial Photography

For this experiment we prepared a 100m string with 5m marks on it and then at the launch site we ran 50m of the string in one direction and then 50m at 90 degrees in another direction. We then placed a set of white coriflute markers at each 5m point and pinned it to the ground with a skewer stick so wind couldn't blow it away. With this setup we were hoping that at least some of the markings would be visible from the air at apogee. We used two different cameras taped to either side of the rocket. One camera had a regular narrower field of view while the other had a wide angle lens.

We again obtained a calibration image for each camera, but this time we located the camera exactly 1m from the wall.

Cameras on the side of rocket

String with markers

Markers set out on the field

Narrow FOV calibration Image

Wide FOV calibration Image

To work out the altitude we simply use ratios of the measurements in the apogee photo vs the calibration image measurements.

For example if in the apogee image we see that 35m on the ground corresponds to 30cm in the calibration image then we can use the following formula to work out how high we are:

1 m / 0.3m = h / 35m h = (1 x 35) / 0.3 h =  116.7m

Altimeters

We used two different altimeters for these flights The peak only reading AltimeterOne and the recording AltimeterThree. These altimeters use barometric pressure sensors to measure altitude down to an accuracy of about 1 foot.

AltimeterOne

AltimeterThree & App

Altimeters Mounted to the side of the rocket

Results

We repeated the experiment on three flights and measured the altitude using all 4 techniques on each flight.

Inclinometer Results

The following angles were observed with the two different inclinometers. They were in quite close agreement with each other. The table also shows the calculated altitude estimate based on the average of the two angles. The inclinometer was located 42.5 meters from the launch pad.

Flight 1 - zero angle

Flight 2 - zero angle

Flight 3 - zero angle

Flight 1 - elevation angle

Flight 2 - elevation angle

Flight 3 - elevation angle

Ground Photography Results

To find the apogee image we watched the flight video frame by frame and paused when the rocket stopped gaining altitude. We then saved this frame to a file. We then overlayed this image with the calibration image and read the altitude off directly. Each small tick mark represents 1 meter in the images below.

Flight 1 with calibration image

Flight 2 with calibration image

Flight 3 with calibration image

After combining the calibration image with the apogee image we arrived at the following altitude estimates:

Aerial Photography Results

The markers on the ground were easily visible in the footage right near apogee. Having the two sets of markers at 90 degrees helped ensure that at least one set wasn't obscured by the rocket. We again reviewed the video for each flight and saved an image when the rocket was near apogee and the ground markers were visible. The narrow FOV camera failed to record the entire flight of Flight #3.

Flight 1 narrow angle

Flight 2 narrow angle

Flight 1 wide angle

Flight 2 wide angle

Flight 3 wide angle

After overlaying the calibration image and rotating it to align with the ground markers we were able to work out the altitude by scaling the readings appropriately. Here are the altitude estimates from the two cameras. The estimates in brackets represent altitude derived from the second set of markers placed at 90 degrees. These are higher because the camera is looking at them from an angle, ie. not directly above them,

Altimeter Results

We flew the AltimeterOne on all three flights, and the AltimeterThree was added on the last flight. We know from past experiments that these are quite accurate, and so we used these readings as the reference for the other measurement techniques.

Analysis

Here is a summary of the measurements. As you can see the inclinometer and ground camera photography have a significant errors in their estimates. This is primarily due to non-vertical flight of the rocket. On the diagram below you can see that if the rocket reaches apogee some distance away from the vertical the apparent elevation angle is not going to correctly represent the true picture. For large elevation angles this error is going to be even more significant.

Rocket flying away from the inclinometer will give lower altitude estimates than the real altitude

Rocket flying towards the inclinometer will give higher altitude estimates than the real altitude.

Averaging altitudes from two different inclinometers located 90 degrees apart gives better results.

Placing the inclinometer further from the launch pad will give better results.

Aerial photography will measure the distance to the feature rather than altitude if the feature is not directly below it.

Ground photography has similar limitations to the inclinometer because the calibration image is taken against a vertical wall.

 

Conclusion

As we can see each of the different techniques produced different altitude estimates for the same flight. When compared to the altimeters the Inclinometer results varied by as much as 30% from the actual altitude. The ground photography technique achieved similar results, while the aerial photography was a little better.

If you are performing experiments where it is very important to measure altitude accurately then altimeters are really your only option, When flying casually and you just want to know approximately how high your rocket went then the other techniques could be used.

Let's have a look at some of the advantages and disadvantages of using each of the techniques.

Flight Details