Crowdsizing the chute

The Aerotech Mustang weighs about 11 ounces (312 grams) without motor (according to Aerotech), and it comes with a 16″ parachute. Is that crazy small, I wondered? Seemed it to me, but then the Mustang’s been in production since 1989 and I’m sure the Aerotech people know more about rocket recovery than I do and I’d think they would have made the chute bigger by now if it were seriously undersized.

But this article from Apogee Peak of Flight says a rocket of that weight should have a 33 inch chute! And the rocketreviews.com Parachute Calculator gives a range of 19 to 38 inches. Those both seem crazy big, except at the low end of the latter.

I started thinking about something I was talking with my son about the other day, which is that if you average estimates of something by a lot of inexpert people, in many cases you get as good an answer as if you consult one or two experts. That led me to this, which is not quite the same thing, but inspired by it.

I assembled a somewhat arbitrary list of 25 rocket kits, one each from 25 manufacturers. (Dynastar and Apogee I counted as two, for what that’s worth.) They ranged in weight from Semroc V-2 (1.3 oz) to RDS Aries (72 oz) with a median weight of 10 oz. Then I plotted stock parachute diameter versus weight, and fit the data to a straight line.

Really I should have used weight including burned out motor, but I wasn’t that ambitious. And I couldn’t figure out a way to make Google spreadsheets display a scatterplot with a fit line, so instead I plotted points along the line in blue along with actual data points in red.image

It looks like a fairly decent fit to a line, which is the first surprise here; the Apogee formula has the area proportional to the weight, or the diameter proportional to the square root of the weight. But clearly no one designs chutes that way: as the weight goes to zero, the diameter doesn’t go to zero. (The smallest chute supplied with any of these kits is 12 inches.)

Then I calculated the percent difference between the actual chute size and the linear fit value:image (2)

The big outlier here is the Dynastar Grappler, a 10 ounce rocket that comes with a 32″ chute. Amusingly, the Apogee NeMSAR’s chute seems to be the most undersized: 12″ for a 5 ounce rocket. Now, part of this is that these rockets are designed for different kinds of flying. The NeMSAR is made to fly as high as 2700 feet on an F motor while the Grappler tops out at about 1200. So it makes some sense to want to recover the NeMSAR faster.

The lightest rockets (at the top of the above chart) are the ones most affected by my neglecting the weight of the motor. Include that and they might fall better on a fit line. Maybe.

As for the Mustang, the fit line gives a diameter of 19.6″ for an 11 ounce rocket. The stock chute is smaller than average, but not much more so than the Pemberton Tech King Kraken or the Public Missiles Mystic.

Of course a different choice of 25 rockets might give different results, but I don’t think they’d differ much as long as they covered a similar weight range. And the whole methodology might be questionable, but the marketplace does seem to favor something like the line I get here. Which, by the way, is

diam = 22.16 + 0.61 (weight - 15.43)

in case you want to mess around with it.

 

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