Flight

The rocket launched on Sunday, June 26th at 9:00 in the morning, flying to 45,482 feet above the ground and breaking the world record for apogee of a high school rocket. It came off the rod at 48 m/s, leaving a straight trail of white smoke behind as it went Mach 1.8 and spent 25 seconds at supersonic speeds. At apogee, the black powder ejection charges went off, but the opening force of the parachute was too strong for the nylon cord and the rocket broke off into free fall. It tumbled to the ground for about five minutes before landing where we were able to recover it mostly in one piece.

2022 Goddard Launch.mp4
First half of rocket flight as recorded by SystemsGo. Cuts out before the parachute fails lol.
Cristian inspects his pants while Karim documents the moment.

Post-Mission Analysis

After we got back to the hotel, we broke out the left over pieces of the rocket to inspect how our hard work had faired. Though some components performed better than expected, we lost a great deal of data, including our payload, which probably drifted about 15 miles down-range inside of our nose cone and lifted by the parachute. All three altimeter/GPS devices output data (which you can read more about here), but the instrumentation which would have told us the pressure and temperature of the ox tank over time did not record any flight data.

Fuel Grain Regression

Our fuel regressed faster than we expected, averaging about 2 mm/s over a 14 second burn. There is a spot on the top left of the photo where it looks like it almost burned through, likely due to the higher O/F ratio and flow rate in the region. The injector pointed at that section was missing when the rocket was recovered, so the flow rate was probably higher due to the injector melting away during the ignition of the rocket. My best guess is that we burned through 6.2 kg of fuel, which is just over half of the 11.2 kg that we loaded (note that I am extremely unsure of this number, I had to add up several components from memory and approximate some numbers that we never measured).

Altitude

Many numbers were called out for the actual apogee, with 49,500 and 49,700 feet above sea level two of the main one. Based on our altimeter data, which appears to be reliable based on the shape and the fact that the two separate altimeters agree relatively well, I would call the actual apogee 47,200 feet. That is 43,300 feet above ground level, which is still a significant improvement on the previous world record for high school rockets of about 36,000 feet.

Peak altitude (in meters) at around 55 seconds.
The Stratologger (orange line) gave us extremely choppy data. It is predicting based entirely on the pressure around the sensor, whereas the Telemetrum reports data using a built-in accelerometer, giving much more accurate results.

Speed

The rocket followed the expected speed curve, although only the Telemetrum with the accelerometer provided any reliable data. It maxed out at about 1700 ft/s and Mach 1.8.

Predictions Comparison

In theory, you could perfectly determine the drag and the thrust of the rocket based off of one flight. If, after the motor burns out, the rocket is at its max speed, (assuming you know the weight), you can calculate what the drag is by your known net force. Using a drag table that you reverse-engineer from that, you can calculate what the actual drag was while the motor was under thrust.

Unfortunately, it looks like our motor was still spitting a little bit of thrust out for about 30 seconds. After that point, the drag data looks pretty accurate to what we predicted. Before that, the calculation for actual drag assuming no thrust is way too low, so I think that the motor didn't quite burn out until 25-30 seconds. The only issue is that I have no idea why the gas-only phase would be ~15 seconds long. Nevertheless, there was a pretty steady white trail behind the rocket up to that point, so that is our best guess.

Graph comparing predictions to actual flight data. I generated it by assuming that my predictions for drag were correct until the motor cuts off at 30 seconds (which is an assumption that is possibly invalid). After that, I display the calculated drag (green line). As you can see, it agrees pretty well with the prediction (purple line).
Predicted thrust compared to the calculated thrust, arbitrarily cutting off at 15 or 30 seconds as the range of when the motor could have stopped firing.

Thrust

The total impulse of the motor can be calculated by integrating the calculated thrust over time. Assuming a 15 second burn time and extremely low drag, it is only ~68.9 kNs, but with the current estimate of a ~30 second burn, it is 79.8 kNs. At either extreme, the motor is well above the threshold for P-class.

This is significantly lower than we predicted, reaching only the total impulse of the bottom 2% of simulations. Although the models included many factors to adjust for imperfections, we still only got about 80% of the thrust that we had predicted the average motor would have. Quite a few issues could have caused the problem - injectors melting, post combustion being too short to properly mitigate combustion efficiency, different regression / ox flow rates, etc. Without any hot-fires and with several new technologies, you can't guarantee anything about the performance of a motor - although we were at least in the ballpark.