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comment by kleinbl00
kleinbl00  ·  12 days ago  ·  link  ·    ·  parent  ·  post: SpinLaunch conducts first test of suborbital accelerator at Spaceport America

'Sokay. We've got a lawn dart, and it's doing more than going up. Now let's look at our friends Spinlaunch and their demo launcher. I'ma use your velocity 'cuz you calculated it and again, lazy. I'm also going to model their demo as a scuba tank because - you guessed it! - lazy. Let's go with an AL80 - 14.2kg, 184mm in diameter, 662mm long. we're going to work backwards from your linear velocity.

SCUBALAUNCH = 14.2kg, 184mm dia, 662mm long

SCUBALAUNCH LINEAR VELOCITY = 800m/s

SCUBALAUNCH RADIUS = 1/3 45m = 15m

SCUBALAUNCH ANGULAR VELOCITY = 509 RPM

Oops, we already have a problem. We know it's designed to go 450 RPM. We also know that "SpinLaunch’s first suborbital flight utilized about 20% of the accelerator’s full power capacity for the launch" which... I mean they been pretty loosey-goosey with terms so I'll bet they mean it was running at 20% of the critter's speed.

SCUBALAUNCH PROBABLE ANGULAR VELOCITY = 108 RPM

SCUBALAUNCH CORRECTED LINEAR VELOCITY = 168 m/s

SCUBALAUNCH CORRECTED FLIGHT TIME = 17.1 s

SCUBALAUNCH CORRECTED ALTITUDE = 1438m

= 4717 ft which, again, is aspirational but looks a lot more like what they actually got on video. And i mean, I can't throw a scuba tank most of a mile into the air so kudos. But I don't really think Spinlaunch can, either. Can they spin a scuba tank in a 15m circle at 108 RPM? mmmmmyeah, I'll bet they can. Can they put that 30m circle under something kind-of vacuum-ish? mmmyeah, I'll bet they can. But you can hear the whirring. It's under vacuum-lite at best.

But let's tie this poor sonofabitch back into our lawn dart.

SCUBALAUNCH LINEAR KINETIC ENERGY = 200kJ

SCUBALAUNCH MOMENT OF INERTIA = 3195 kg/m^2

SCUBALAUNCH ROTATIONAL KINETIC ENERGY = 772,000 kJ

...this is getting foreboding. That's 215 kW/h. We'll bleed off our pathetic 200kJ and be left with... about the same. We're going to swap our 3195 kg/m^2 moment of inertia for...much less..

NEW SCUBALAUNCH MOMENT OF INERTIA = 0.548 kg/m^2

SCUBALAUNCH SUICIDAL URGE = 8844 Hz

Now. this is about where I argue, often ad nauseum, that the model is broken. 214kW/h is a lot of energy to put into a scuba tank. 15m is a hell of a lever arm. But there is no way in hell you're going to get a 9kHz flat spin out of a scuba tank. Ever. Under any natural, normal circumstances.

But you're also not going to get zero.

Conservation of angular momentum means the lion's share of energy you're pumping into the system stays with you. And it does so in an inconvenient form. Never mind any counterweight you may have, you're pouring the majority of your energy into you, not your launcher and you don't have a convenient way to deal with it. Worse than that you inherit it all at once when you fling your scuba tank into space.

You can't get rid of it easily, either. I mean, you could keep your scuba tank from rotating with a linkage. You would then turn it into a cocktail shaker, unfortunately, and shaking your cocktail at 107 cycles per second (never mind 450) is going to be bad for your cargo ("jerk"). But Isaac won't be cheated - the conversion between one kind of motion and another conserves momentum and there is much in this system.





kleinbl00  ·  12 days ago  ·  link  ·  

I ran the numbers for Spinlaunch's actual system. This is left as an exercise for the student. What you need to know is it's at a 45m arm, it weighs 11,200 kg, it's 25 feet long and prolly 3-4 feet in diameter. It's "suicidal urge" is gobsmacking.

And again. Those aren't real numbers. But there AREN'T ANY REAL NUMBERS AROUND SPINLAUNCH. In order to get to that math you're spinning a pair of orcas around a 45m circle at 450 rpm and then flinging them into the air at Mach 6. I mean, c'mon. Presume you build this thing out of rainbows and hope, dumb-ass dynamics is still slapping you down. A half-gram USB-C connector under 10,000g weighs this:

Design for that. Go ahead. Design for it in not one axis, not two axes, but the transition between those two axes. Also tell me you're going to aerodynamically stabilize a two-body problem with this thing.

I don't know what kinda yaw is recoverable at transsonic speeds but I'll bet those are heroic calculations, too.

And it kinda feels like this is more math than has ever been done around Spinlaunch.

kleinbl00  ·  11 days ago  ·  link  ·  

so holy shit y'all

- the accepted rotational velocity of a frisbee is like 2300 RPM

- the accepted rotational velocity of a discus is like 400 RPM

- the accepted rotational velocity of a clay pigeon is 2-3000 RPM

So while I'm keenly uncomfortable with the idea of a lawn dart spinning through the sky at 146 Hz is 8700 RPM, I'm 100% A-OK with a frisbee doing 2300.

So... maybe the difference between the lawn dart's suicidal urge and the lawn dart's reasonable behavior is the aerodynamics of the lawn dart.

This does not portend well for the rest of the math.