# Captain, that is illogical

I swear, for a hobby that’s supposed to be all about precision and engineering and physics (OK, and aesthetics too), we have some real numerical stupidities we can’t get rid of.

Like the A8-3 motor. “A” refers to impulse class, it’s supposed to mean the motor has a total impulse of 1.25 to 2.50 N-s. And indeed, according to NAR S&T, its impulse is 2.32 N-s. So far so good. And the “8” means average thrust of 8 N. And S&T says its average thrust is… 3.18 N.

What? That’s well under half what it’s “supposed to” be.

I’ve never seen an explanation of this that makes any sense. And as I understand it, present-day NAR certification rules say the motor designation has to be accurate, at least to a much better level than this; but the Estes A8-3 is grandfathered, so they can continue calling it that, even though it’s really an A3-3. (Which is arguably for the best, considering how many Estes instruction sheets are out there saying to use an A8-3 motor; changing the designation to A3-3 would cause havoc.)

Similarly the Estes C6-5 has average thrust 4.74 N. The Quest C6-5: 3.45 N. Same shorthand designation, but the Quest has about 25% less thrust. If you have a rocket you usually fly on the Estes and you think you can swap in a Quest, you might be in for a surprise. (Moral: Use the thrust curves. Run sims.)

Then there’s impulse percentages. Anything between 160 and 320 N-s is an H motor, but you might want more precision than that; so if you have a 240 N-s motor, you call it a “50% H”.

It’s called “50%” because it’s “halfway” between the minimum and maximum impulse for an H. As a formula, where “J” stands for impulse (don’t look at me, that’s the usual symbol):

%=100((J–J_min)/(J_max–J_min))

So for this example: 100((240–160)/(320–160))=50.

“50% H” means the same thing as “240 N-s” and is supposed to be easier to understand. But it’s dumb terminology, because it sounds like it means 50% of 160 to 320 N-s, i.e. 80 to 160 N-s, i.e. a G motor. Do two 50% H motors make a 100% H motor? No, they make a 50% I motor. For something that’s supposed to be easier to understand, it’s certainly more confusing.

Besides that, it’s inconsistent.

We label motors on a logarithmic scale. That just means B is twice A, C is twice B, and so on. Or to put it in a formula: Take the total impulse, divide by 0.625 N-s, and take the base 2 logarithm. (Which is just the logarithm —base 10 or natural log or whatever base you want — divided by the logarithm of 2 in the same base.) In our example, log(240/0.625) / log(2) = 8.585. Now take the integer part of that — 8 — and use the corresponding letter: A=1, B=2, C=3… H=8. So it’s an H motor. If it were 160.01 N-s you’d get 8.000 and if it were 319.99 you’d get 8.999.

But on this logarithmic scale, where does our motor lie between a minimum and maximum H? 0.585 above the minimum, that’s where. So really it should be a 59% H!

Which is even more confusing terminology of course. If you’re going to think along these lines, better to come up with a unit corresponding to the base 2 logarithm of impulse divided by 0.625 N-s — we can call it a stine, maybe — and then say this is an 8.585 stine motor. There, it’s precise, it doesn’t abuse the concept of “50%”, and it’s easy to remember an 8.585 stine motor is an H while a 7.318 stine motor is a G, and so on.

Of course, two 8.585 stines are not a 17.170 stine. In fact they’re a 9.585 stine.

Whatever you do is going to confuse someone. Anyway, the horse got stolen long ago, no point in reconsidering the barn door. Or something. Just grit your teeth and put up with this “50% H” nonsense… or just talk in N-s.