Kinetic Launch Skydiving

[alxian]

remember back in your childhood (or on tv for some of us) when you saw the dude being shot out of a cannon?

 

[ Inspriration ]

 

what if instead of wasting 30 minutes or more in a plane you could get up to 91 and a half hundred meters you could get shot out of a linear magnetic accelerator (vertically), encased in a plastic shell [wind breaker](recoverable if you can find them, with GPS recievers in 'em to help in that recovery).

 

could a human survive the acceleration? (say 5-7 gees, over a few seconds of acceleration, they'd need a pressure suit to fight the blood being forced out of their heads lest they be knocked out at the apex of their jump.)

 

travelling straight up for a half dozen seconds to reach an ideal drop height of between 20k-30k feet? (a little can of compressed air an accelerometer and an altimeter controlling when the shell is cracked open beginning your descent)(either with a conventional suit, bird/superman suit, airboard, or full blown hang-gliding apparatus [to fall with style])

 

i'm not very good at the math, but how much acceleration would a person need to get up to 9100 meters against the pull of gravity.

 

a person could jump many more times than climbing into the sky aboard a dinky plane.

[UncleAl]

i'm not very good at the math, but how much acceleration would a person need to get up to 9100 meters against the pull of gravity.

Ignore air resistance, assume a vertical shot. A 70 kg body at 9100 meters has gravitational potential energy of

 

PE = mgh

PE = (70)(9.8)(9100)

PE = 6.24x10^6 joules

 

You need the same starting kinetic energy,

 

KE = (mv^2)/2

v = sqrt [(2)(KE)/m)

v = sqrt [(2)(6.24x10^6)/(70)]

v = 422 m/sec or 944 mph

 

(Note that mass cancels, as it should). The speed of sound is 770 mph. Air resistance will not be zero traveling at the top speed of a very hot load .357 magnum bullet. Ignoring air resistance and given a 30 meter (98 foot, 10 story) vertical launch tube, the average speed from dead stop to finish of acceleration will be 211 m/sec,

 

s = vt

t = s/v

t = 30/211

t = 0.142 sec

 

s = (at^2)/2

a = 2s/t^2

a = (2)(30)/(0.142)^2

a = 2968 m/sec^2 or 302.9 gees

 

You will need 304 gees, the extra gee canceling ambient gravity. CRUNCH, even shooting into vacuum.

[alxian]

WOW :hihi:, 304 gees ?!?!?! :hihi:, thanks uncle AL, however those numbers seem slightly excessive.. and a human occupant very likely to become soup in the attempt :evil: .

 

i had a little help from a fellow employee with the acceleration from a dead stop a distance of 9100 meters (an altitude of 30000 feet where velocity would be nil momentum spent). surely making that trip in a dozen seconds (9100 meters) would be torturous but by those figures it would be comically lethal. a simple calculation points toward 2:30 seconds being the border line speed required (at a constant velocity) to even get to 9100 meters ignoring the extra gee of gravity (that a human body would tolerate in a flight suit)... since acceleration is not continuous the capsule may in fact need to be accelerated to a crushing initial velocity of some ~3 km/s before leaving the launcher..

 

i however like the idea of a 100 foot launch tower and was doing some fun brainstorming on how it could be powered most cheaply. being a collapsable structure needing to launch several times in a very short period of time then dismantled and hidden inside a small convoy of "white vans". also having a half dozen or more launchers in the same field for formation dropsmay prove difficult to power for recreational purposes. pneumatics are out, and it would take quite a bit of juice to power each launch.

 

looks like the flights will have to be supplimented because an initial acceleration of 58.8 m/s isn't going to do the job, and neither is the necessary if your estimate of the necessary acceleration 3+ km/s, some 300+ gees may be accurate... but that would mean at 211 m/s a 43 second flight far more than the dozen seconds i had hastily guesstimated.

 

chemical rocket motors could be an answer, however strapping 3-4 of them to the capsule with the promise of a very uncomfortable ride isn't likely to offset the extreme dangers of launching ones self skyward on magnets and a prayer..

 

*frown. looks like i'll have to ponder this one a little more.

 

upon some reflection perhaps 30K may not be necessary, as the flight time is decreased perhaps so too should the fun time. launching to below 10k feet while not reducing the velocity to a survivable level would mean for each plane drop you could get several kinetic launch drops in and still have time for tea before the plane even reached altitude...hmmmm.

 

10k feet, ~3 km, just under a minute at an average acceleration of 58.8 m/s (6gees), if that speed is only initial how far up would the capsule get? wouldn't crack 5 thousand feet... *sigh.. getting closer

[Dark Mind]

Always amazes me how much energy humans are willing to put into something that will probably never be... At least in their life times :).

 

But that is the joy of science I suppose :D. Just look at my threads on Perpetual Motion :eek2:.

[CraigD]

What a cool idea! Given the moderate financial success of "extreme rides" such as bungee jumping, you just might be able to actually do this, and maybe even show enough money-making potential to get VCs to pay.

 

Getting down to numbers.

For starters, 10 km is way too ambitious a target altitude - only record-attempters and unfortunate military pilots ever jump from this height. Recreational skydivers usually jump from 1500 to 4500 m (the last gives a good 60+ second of safe freefall).

 

So what can a 100 meter long super-human-cannon/railgun achieve?

 

Most of the sources I checked say that a healthy person can withstand about 9 gs for up to 2 sec. Some put the number for a specially trained person as high as 15gs.

Calculating for both (and subtracting a g of actual acceleration due to the force of gravity, we have (all in units of meters and seconds):

a1= 76 136

t1=(2*d1/a1)^.5

v1=t1*a1=

(2*d1*a1)^.5= 123 165

pretty respectible "muzzle velocities".

Without air resistance, this gives max altitudes of 872 1489

pretty close to recreational skydiving altitudes.

 

Unfortunately, air resistance has a major effect on person-size/mass projectiles. Taking 135 m/s as the fastest freefall speed achieved by a human (higher speeds have been claimed, but not demonstrated in front of reliable witnesses), and calculating a combined drag coefficient (cf) from that, then using numeric methods in the form of this bit of M code

s m=100,cf=.055,d=100,v=123,t=0,dt=.01
f  s a=v**2*cf/m+9.8,d=v*dt/2+d,v=-a*dt+v,d=v*dt/2+d,t=t+dt i v<0 w t,?10,d,?40,v,! q
s cf=.325,t=0,d0=700
f  s a=v**2*-cf/m+9.8,d=v*dt/2+d,v=-a*dt+v,d=v*dt/2+d,t=t+dt i d<d0 w t,?10,d,?40,v,! q:d0=0  s d0=$s(d0=700:200,1:0)

gives the following (prettied up by hand):

Description__Mass___Drag__Vel___Alt__Time:_Up__700__200___0

Vacuum_____________0______123___872________13____6___12__13

__________________________165__1489________17___13___16__17

Spread_____________0.325__123___375_________6_________7__11

__________________________165___454_________7_________8__12

Diving________100__0.055__123___659________10________12__16

__________________________165___943________12____8___17__21

Light_faring__100__0.02___123___772________11____4___14__18

__________________________165__1204________14___13___22__26

Heavy_faring__250_________123___828________12____5___15__19

__________________________165__1354________16___16___25__29

Vehicle______2000_________135___866________12____6___16__20

__________________________165__1470________17___18___27__31

Units are kilograms, meters, and seconds.

”Spread” means the skydiver is launched in the “spread eagle” position usually used while freefalling.

“Diving” means he’s launched in the aerodynamic dive position skydivers used to descend quickly

The various “farings” mean the skydiver is enclosed in an aerodynamic shell.

“Vehicle” means the skydiver is enclosed in a thin, rocket-shaped vehicle weighting about as much as a small truck.

 

Skydiving organizations insist on a minimum opening height of 700-1000 m, but with the right equipment, a 200 m opening height would probably be safe, so freefall times to those heights, as well as a “splat” height of 0, are shown.

 

So it looks to me as if the system alxian describes could be built to achieve a freefall experience substantially shorter than jumping from an airplane, but still enjoyable, without injuring the skydiver/human cannonball. Not only that, they’d enjoy the never-before-done experience of “skydiving up”.

[Dark Mind]

Nice :eek2:...

 

Excellent post.