[pygame] Rocket + Bike = Physics

["Ian Mallett" <geometrian@xxxxxxxxx>]

Hello,

A little bit ago a idea of attaching a rocket to bike came up (Thank you JP)
The pygame community is a fun-loving group, so in the interest of fun, let's talk about the implications of it in a TOTALLY off-topic thread.  :D  I encourage responses, as I think they will be to the amusement of all concerned.

I'll start.
Yanom points out that the size of these things is pretty big and hence a rocket bike would really be "more like attaching your bike to the rocket."  Because of the bike part, I'm assuming all propulsion is lateral.  Let's likewise assume that a) the rocket can support itself horizontally this way, and b) the bike can hold the whole thing up as well on it's small two wheels.  We're not working against gravity here, so acceleration is going to be considerably higher.  The Atlas V, the rocket mentioned, masses 546,700kg.  A bike masses < about 20kg.  The total mass of the apparatus = 546,720kg.  The first stage of the rocket exerts 4,152,000N of force over a 253 second burn time.  Let's assume friction is negligible--(and duh, we're going to ignite it).  

F = MA says that we'll accelerate at approximately 0.77 G (darn was hoping for something more) But:
After 253 seconds, we'll be traveling at about 1.9 kilometers/second = 5.6 mach, or fast enough to cross the continental US in about 35 minutes.  

BUT...the fuel burned lightens the payload (more specifically, "thrown" out the back, thereby pushing the rocket forward (Newton's Third Law)) so we actually go faster.  
This kicks us up to over 2.7 km/second = 8 mach, or fast enough to cross the continental US is about 24 minutes.  
At the highest acceleration, we get a more severe, but certainly tolerable 1.6 Gs.  
See attachment for the program I used to derive this.  I didn't bother to do calculus--a second by second approximation is good enough.  

I actually thought of putting four rockets on this guy so it's balanced--a bike with a rocket on one side would be lopsided, duh.  Again, for all you practical people, shut up :-)  Turns out though that the acceleration remains nearly the same, which I should have known if I'd thought about it.  Oh well.  

Now, how fast are the bike wheels spinning?  At 2.7 km/second, and a wheel diameter of 559mm (this is a mountain bike) each wheel will spin at 165,540 RPM, which would probably cause a violation of the wheel's structural integrity and a catastrophic failure, i.e., the wheel would explode.  

All this is interesting, but boring, if you know what I mean--so let's calculate what happens when our contraption (let's use the four rocket variety) crashes headlong into an invincible wall traveling at 2.7 km/second.  The total mass just before impact is approximately 1,053,841kg, and it's traveling at a good 2.708km/sec.  This means that at impact, we have a kinetic energy of 3,864,047,133,512j or about 3.8 terajoules.  Now we're getting somewhere fun!  This collision is comparable in scale to a small atomic bomb.  Now, as far as acceleration goes, a bike is pretty short, say 2.5m.  When you sit on it, you're probably not longer than 1m yourself, meaning you'll come to a full stop in about 0.369 milliseconds, equaling a brain-splattering 748,852Gs, which would very probably kill you.  Moral: don't ride bikes with big rockets into immovable objects.  

Which is not to say it isn't done--at least attaching rockets to bikes.  Actually, the smaller rockets probably work better for pure acceleration.  This video uses several small rockets and accelerates to 163 m/s in about 5 seconds.  French people on rocket bikes is always fun.  Then there's completely random stuff getting shoved by rockets, like buses (rocket only helps here), skateboards, small cars and real cars.  This German rocket car is a fizzle.  An unmanned rocket car is launched peculiarly here.  Water rocket cars still go fast, and for our grand finale, in '76 someone tried to jump the St. Lawrence River with a rocket powered Lincoln Continental (skip to 2:55), which pretty much disintegrated in midair.

Ian
#Atlas V Rocket + Bike = Rocket Bike
Thrust = 4152000.0

BikeMass = 20
PersonMass = 64.9 #This is my actual mass, by the way.  Substitute yours as you see fit.
DuctTapeMass = 1 #We gotta hold this thing on, right?
BodyMass = 262250
FuelMass = 284450.0

Time = 253.0

Speed = 0.0

MassLoss = FuelMass/Time

for second in xrange(int(Time)):
    #F = MA (Newton's Second Law)
    #Thrust = Mass*A (Mass changes based on time).
    TotalMass = BikeMass + PersonMass + DuctTapeMass + BodyMass + FuelMass
    Acceleration = Thrust/TotalMass
    FuelMass -= MassLoss
    Speed += Acceleration
    print 'T %isec.   Speed %fm/s   Acceleration %fm/s*s = %f"G"s' % (second+1,Speed,Acceleration,Acceleration/9.8)