What's this all about?

While I was at the 2001 Nationals I took advantage of the opportunity to gather some data on mtas. I measured booms from Gary Broadbent, Chet Snouffer, Nobu, Jason Smucker, and a lot more. In all, a total of 65 booms.

I didn't gather the data with the expectation that I would be able to develop any kind of comprehensive model of how an mta works. My hope was that in looking at the data it might be possible to compare different designs and identify some general patterns.

You know that old saying: "What goes up, must come down"? I think it touches on two factors that are important to mta performance. One is how far they go up, the other is how slow they come down. Let's start with looking at how slow they come down.

Wing Loading

Everything else being equal, a heavier boomerang will descend faster and a lighter boomerang will descend slower. If you're comparing two boomerangs of the same design that have been optimally tuned, all you have to look at is weight. But if you're comparing two different designs, how do you take into account their different sizes?

Wing loading is the amount of weight per unit area of wing. Everything else being equal, a boomerang with a higher wing loading will descend faster, and a boomerang with a lower wing loading will descend slower. Wing loading allows us to compare different designs to see how well they "float" relative to one another.

In order to gather the data necessary to calculate wing loadings, I traced outlines of each design on quadrille graph paper and then counted the squares to estimate the area. This only needs to be done once for a given design, but different boomerangs of the same design aren't identical in weight, so each boomerang of a given design is weighed.

The following table contains a summary of the collected data. For each design it lists: the material used, the range of weights observed, and the wing area.

Design	Material	Weight (grams)	Area (square cm)
Wind Free	Composite	12.5 to 15.5	77.4
Quirl	Phenolic	16.5	94.2
Gradus	Composite	16.5 to 18.3	97.4
Midge	Composite	14.8 to 18.1	99.3
Highlander	Composite	14.7 to 17.0	102.6
Snake, 88%	Phenolic	23.0 to 24.3	109.7
Bonas I	Composite	18.4 to 19.0	116.1
Bonas II	Composite	16.1 to 17.6	116.1
Bonas III	Composite	15.2 to 15.9	116.1
Jonas, Black	Composite	16.8 to 20.6	116.1
Jonas, Yellow	Composite	13.3 to 13.7	116.1
Rod Jones	Plywood	20.5	121.9
Snake, 100%	Phenolic	33.2 to 35.9	132.2
AboSteve	Plywood	35.7	168.3
Bailey	Plywood	38.0	174.8

The next step is to divide the weights measured for each design by the area for the design. The results are graphed below. Lower numbers indicate a boomerang that comes down slower.

The graph seems to roughly correlate with my observations, which leads me to believe that this is a useful first-order approximation of how slowly a boomerang floats down. There are probably some variations, and I wouldn't use it for any kind of absolute ranking, but the general trend seems clear: booms with lower wing loadings float better.

Note that just because a boom has a higher wing loading does not make it a poor choice. This is just one dimension of what goes into the overall performance. Both small and large snakes have high wing loadings, but they certainly see their share of air time at tournaments. This brings us to the other factor: how far they go up.

Deceleration

One of the factors that bears on how high an mta will go is how fast it slows down. Booms that decelerate quickly don't climb as long as those which decelerate slowly, so they don't get a shot at as much height.

From physics we know that F = ma. What we're interested in is the (negative) acceleration of the boom, so if we divide the force of drag slowing the boom down by its weight we end up with something that relates to how fast the boom decelerates.

I'm assuming that the biggest contributor to the deceleration of the boom is profile drag, so that's all we'll look at here. To determine profile drag, we need to know the average frontal surface area exposed to the oncoming airflow. I measured the maximum width, minimum width, and thickness of each design. I took the average of the widths and multiplied by the thickness to obtain an estimate of the frontal surface area. The following table lists the results.

Design	Max Width (cm)	Min Width (cm)	Thickness (cm)	Area (cm^2)
Quirl	27.4	14.7	.150	3.16
Wind Free	29.4	13.0	.150	3.18
Snake, 88%	31.5	13.6	.170	3.83
Bonas III	36.7	15.6	.168	4.39
Bonas II	36.7	15.6	.180	4.71
Snake, 100%	35.1	15.0	.190	4.76
Midge	33.8	15.0	.200	4.88
Jonas	36.7	15.6	.200	5.23
Bonas I	36.7	15.6	.200	5.23
Gradus	33.3	12.9	.305	7.05
Bailey	42.1	18.1	.318	9.56
AboSteve	42.8	17.1	.330	9.89

I read somewhere that drag is proportional to the square of the frontal surface area (can anyone confirm this?). The next step is to divide the square of the frontal area for each design by the range of weights measured for that design. The resulting values relate to how quickly the booms decelerate. Higher numbers slow down faster than lower numbers. The results are graphed below.

Again, the graph seems to roughly correlate with my observations, which leads me to believe that this is a useful first-order approximation of the rate at which a boom decelerates. The booms I see go farthest out and highest are all at the left end of the graph. The general trend seems clear: booms which decelerate slower achieve higher heights.

Side note: doing this graph with LD designs would be interesting.

Conclusions

The deceleration graph explains why, even though they have some of the highest wing loadings, snakes are so prevelent in competition. They simply have more "punch" than almost every other boom, so they get a lot of height and distance out in front. They may come down faster, but they start off higher up as well. The quirl is about the same in this category, but has lower wing loading, so one would expect snakes and quirls to get similar height, but quirls to come down slower.

It's worth noting here that just because a boom decelerates quickly doesn't mean it's a poor choice. Booms that decelerate quickly are going to "damp out" the effects of a bad throw more than ones that decelerate slowly. In competition, where you have a limited number of throws, having a boom that'll forgive your mistakes may be more important than more height.

I think a combination of factors makes the Jonas and Bonas booms so popular in competition. They have low wing loading, so they make good use of whatever lift is present, and due to their rate of deceleration they don't require a perfect throw, which makes them reliable for a broad range of throwers.