Sunday, August 26, 2018

Time to do some TARC math!

Now that the Reliant is finished, it's time to figure out the size of the parachutes needed to land the booster and payload sections safely. To do so, you need to measure the weights of both these sections, which in my case are 178 and 318 grams, respectively. The booster is easy, as one can choose the descent rate and size the parachute accordingly. A "safe" descent rate - one that avoids damage to the fins - is usually around 15 feet per second, so we go to one of several handy-dandy parachute descent rate calculators available on the Internet - I use either Model Rocket Parachute Descent Rate Calculator or Descent Rate Calculator - Rocket Reviews or an app I have on my iPhone. All 3 give similar results, so the choice does not really matter.

But, wait... Why can't we just use Open Rocket, as that's the design program? It gives descent rates, doesn't it?

Yes, but Open Rocket cannot handle the case where the payload section comes down separately from the other section. So what it will give you is a descent rate based on the sum of the areas of all your parachutes and the total weight of the rocket. That's not going to work this year. So we are going to have to do things outside of the simulator. If you use Rocksim, you can trick it into handling this year's TARC circumstances by creating a 2 stage rocket and designating the payload section as a motorless upper stage; you can then attach a recovery device to each stage and set the deployment circumstances. However, most folks don't have Rocksim.

Now I'm ready to do the compute the booster chute size, so I bring up the RocketReviews calculator and put in the booster weight. I prefer to use Top Flight thin mil rip stop nylon parachutes, which are hexagonal in shape, so I choose "hexagonal" from the Parachute Shape drop down menu. Just for grins, I put in the altitude goal of 856 feet, and finally make a guess at the right parachute size before I click the "Submit" button:

Click to enlarge.
It appears that my initial guess of 15 inches was too small - the calculator is recommending a parachute size of 18 inches. Recalculating with this value yields

Click to enlarge.
This is pretty close to my desired descent rate of 15 feet per second, so I'll run with it. My booster parachute will be an 18" Top Flight, bright orange in color.

Now for the harder part - the two identically-sized parachutes attached to the payload section carrying the eggs and altimeter. To calculate this, we must first figure out the required descent rate to land the payload section 43 to 46 seconds after liftoff, which means we have to go to our simulations to get the time of ejection, and subtract that from the duration goal to get the length of time the parachute is deployed. Open Rocket tells me that it will take about 7 seconds to reach 856 feet, so I will subtract that value from the midpoint of the duration goal - 44.5 seconds - to get the parachute time. The descent rate - in feet per second - is simply the altitude (856 feet) divided by the parachute time (37.5 seconds), or
So we need 2 parachutes that will lower the payload section at 22.8 feet per second. Now I go back to the descent rate calculator and put in the weight of the payload section, keeping everything else the same:

Click to enlarge.
Turns out that 18" is pretty close, with a descent rate of 22.6 feet per second. If I fiddle a bit, I end up with a parachute size of 17.8".

However, I need two parachutes, not one, so how do I do that? What I need to do is divide the area of the above by 2 to get the area of each identical chute. Since area goes as the square of the diameter, this means I must divide the diameter by the square root of 2 to get the size of my chutes. Doing so gives me a diameter of 12.6". I can check my work by doing a comparison:
which is close enough for government work.

Trouble is, there are no 12.6" commercially available rip stop nylon parachutes. The closest match is the 12" diameter. So what happens if I use that? Well, 2 12" parachutes have a scaled area (I'm leaving out the factor of pi) of 288, which translates to a diameter of square root of 288, or 17.0". I can now plug this value in into the descent rate calculator, which gives:

Click to enlarge.
This shaves about 1 second off the time, but it is still within the allowed duration range. Quite acceptable, especially given that I really don't want to have to learn to make nylon parachutes. Therefore, Reliant's booster will be recovered by an 18" parachute and the payload section will be brought down by two 12" chutes.

This concludes today's TARC exercise.

No comments:

Post a Comment