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Pneumatic limbs in Zero G

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Sun, 2013-11-03 00:24

Nebelwerfer41 Nebelwerfer41's picture

Pneumatic limbs in Zero G

We had an odd situation come up in a game in which my synthmorph with pneumatic limbs wanted to use his legs to launch himself forward in zero g. How fast would he move in one turn that way? I tried to work it out with my rusty high school physics, but couldn't quite get there. Firstly, I have no idea how much a Steel morph weighs (is 300 kg a safe assumption)? Any help?

Sun, 2013-11-03 12:45

bibliophile20 bibliophile20's picture

Due to advanced composites, a

Due to advanced composites, a (mostly stock) Steel morph probably weights just about as much as an organic person, maybe somewhat more, but certainly not 3-6x the normal 50-100 kg that a normal person masses! (think of all of the extra fuel that you'd have to burn to accelerate synthmorphs via spacecraft if that was the case, and of the massive advantage they'd have in melee combat if they did). As for how powerful the pnuematics are, they're as powerful as you decide they can be, within realistic limits--keeping in mind the current situation. The book mentions "over 7,000 newtons of force". One newton is the force required to accelerate one kilogram by 1 meter per second per second. Since this is a one-time addition of force, giving someone weighing 100 kg a 7000 newton push is 70 meters per second, or a one time, instantaneous acceleration of just over 7 g. But what about the ground he's pushing off against? Is it well secured or sufficiently massive, or will it drift, absorbing a noticeable portion of his new momentum? What's the local escape velocity (for situations with microgravity and small asteroids)? Critical failures here can be fun!

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Sun, 2013-11-03 16:11

LatwPIAT

Nebelwerfer41 wrote:We had an

Nebelwerfer41 wrote:
We had an odd situation come up in a game in which my synthmorph with pneumatic limbs wanted to use his legs to launch himself forward in zero g. How fast would he move in one turn that way? I tried to work it out with my rusty high school physics, but couldn't quite get there. Firstly, I have no idea how much a Steel morph weighs (is 300 kg a safe assumption)? Any help?

Vertical jumping height for all morphs is always 1 meter. (Regardless of gravity... but I assume that's a rules-oversight) If they have penumatic limbs, it becomes "over 2 meters". Using the Newtonic equations for dragless parabolic motion, this means that a normal morph can accelerate itself to sqrt(2m*g) when jumping, or a velocity roughly 4.5 m/s. For a two-meter jump, this becomes equivalent to acceleration to 2*sqrt(g*m), or about 6 m/s. Given 7000 N of thrust on the pneumatic limbs, and the given acceleration in Earth gravity, Newton's second law gives a mass of 1117 kg for any random synth augmented with pneumatic limbs. Yare yare, that is a heavy morph! Especially given that this applies as much to a Case as it does to a Steel with Heavy Synthmorph Combat Armor. Incidentally, this tells us that that a synthmorph without pneumatic limbs can jump with a force of about 5000 N! It's probably more reasonable to say that the mass of a morph is proportional to its DUR, with a constant of 62 kg = 30 DUR. (Using the average mass of a human being, and the DUR of a flat); this would make the DUR 40 Steel have a mass of about 83 kg. With a thrust of 7000 N, this would allow a Steel with pneumatic limbs to accelerate to a velocity of about 85 meters per second! Both of these estimates seem wildly off; using the given jumping heights makes all the synthmorphs incredibly heavy, and making mass proportional to DUR makes them jump incredibly high. It could of course be that the 7000 N of force have a very low impulse, and are best for slow lifting, while jumping is limited to a lower-force, higher-impulse burst, but the text doesn't offer much elaboration in this case. For the record, according to the 1995 [i]Ghost in the Shell[/i] film, a full-body cyborg has a mass of 450 kg. Jumping with a force of 7000 N would accelerate it to a velocity of about 15.6 m/s.

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Mon, 2013-11-04 08:37

Smokeskin

LatwPIAT wrote:

LatwPIAT wrote:
Given 7000 N of thrust on the pneumatic limbs, and the given acceleration in Earth gravity, Newton's second law gives a mass of 1117 kg for any random synth augmented with pneumatic limbs.

No. At 1117kg you can't even walk in standard gravity if you only have 7000N to work with. Let d be the displacement of the pneumatic limb where it delivers the full 7000N, let us say 0.5 meters. Then d = 1/2 * a * t^2, where a is the net acceleration (ie the acceleration from the limb a' minus gravity = 10m/s^2, so a = a' - g) and t is the time the synth is in contact with the floor and able to exert the force from the pneumatic limb. a' = F/m, where F is 7000N and for let us say m = 140kg, so a' = 50 m/s^2. a = a' - g = 40m/s^2 This gives us t = sqrt(1m / 40m/s^2) = 0.16s. Given a = 40m/s^2 this gives us v = a*t = 6.32 m/s, for a jump height of 2 meters. 100kg of mass gives 3m jump height, 70kg gives 4.5. The 450kg GitS cyborg gets to jump an impressive 28 centimeters :) Give them 50.000N and they can jump 5 meters.

Mon, 2013-11-11 16:02

Nebelwerfer41 Nebelwerfer41's picture

Thanks everyone for the

Thanks everyone for the replies. I knew that the mass was the one variable I didn't have. BTW, I would have been pushing off of the inside of a space station, so I would definitely achieve velocity relative to the surroundings. Thanks for going the extra mile and crunching the numbers on mass relative to the jumping height listed in the book. To recap so we have the numbers right, you need to be 140 kg in order to achieve a 2m jump with 7000n of force, correct? Given a mass of 140 kg, you can go 50 m/s by propelling yourself with 7000N of force, right?

Mon, 2013-11-11 17:14

LatwPIAT

Well, using a more accurate

Well, using a more accurate estimate of g = 9.81 ms^-2, you can probably go as high as 178 kg and still jump 2 meters up under the assumption of a 0.5 meter displacement. This will let you reach speeds of 49 m/s in zero gravity. Of course, this all depends on the distance over which you can work that force; if you can double the displacement, you can also double the maximum mass. If you can exert force over half a meter of distance when jumping, your maximum mass is 178 kg. Exert force over a full metre, and you can have a maximum mass of about 357 kg. This is for maximum masses; have less mass and the same force, and suddenly it's a lot easier to jump higher and move faster.

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Tue, 2013-11-12 14:19

Smokeskin

Nebelwerfer41 wrote:To recap

Nebelwerfer41 wrote:
To recap so we have the numbers right, you need to be 140 kg in order to achieve a 2m jump with 7000n of force, correct?

In 1 g, yes.

Nebelwerfer41 wrote:
Given a mass of 140 kg, you can go 50 m/s by propelling yourself with 7000N of force, right?

No. While pushing with 7000N you get 50m/s^2 of acceleration. If your legs allow you to push 0.5 meters you'll be in contact with the surface for t = sqrt(2 * 0.5m / 50m/s^2) = 0.14 seconds, which at 50m/s^2 gives you a speed of just over 7m/s. If you want to get to 50m/s and we upgraded the 140kg synth to have special legs that could displace 1m, they would still need 175,000N to do the trick.