Warfare Plane and Tank
Date: June 2004
Okay, this is kind of a stupid question, but I know this
group of programmers making an Real-Time Simulation strategy game(army
commander game), and it was suggested that, within the futuristic
setting, it'd be possible to have a stationary tank fire a grappling hookto catch a
passing aircraft, thus causing it to crash.
There are a few problems arising from this, but the main one contended is
what happens in the event that 1: the tank does not immediately break, 2:
the aircraft does not immediately break, and 3: the cable does not
One side contends that the tank could be yanked straight off the ground,
in the event that either
1:the plane's wings generated enough more lift than the combined weight of
2: if the plane's trajectory was not parallel to the surface the tank was
on(the pilot "pulls up"), and the power plant of the plane was strong
enough to pull the combination upwards faster than the force of gravity
This side further contends that, if the plane's trajectory was perfectly
horizontal, the tank would simply be dragged along the ground as the
aircraft followed a pendulum arc using the tank as a center of rotation,
thus crashing 100% of the perfectly horizontal travelling planes captured.
The other side contends that, by the simplicity of newton's law, the tank
would immediately leap into the air, regardless of the plane's lift, even
if the plane is travelling at a perfectly horizontal trajectory, thus
guaranteeing that 100% of such attacks would be ultimately fatal for the
tank in question.
As a side note, what would be the calculation for whether or not any of
the parts broke?
The answer is, simulate all parts adequately and you'll get your "game answer".
Most of your conjectures could be made more realistic by back-of-envelope calculations
from some specific numbers.
Your plane has an ascribed mass and speed and thrust,
the tank has an ascribed mass,
the cable has a specific reasonable strength and diameter and stretchiness,
and must all be stored on the tank and pulled up by the hook,
and the hook has a projectile speed which is not enormously faster than the airplane
and gets slower as the cord unwinds.
Reels which go from standing still to 2000fps are slightly uncommon. ;-)
Steel cable's strength is maybe 150kpsi, so a cable which lifts a 20-ton tank with 2x margin
needs to be at least 0.5 square inch, or 0.7 inch thick. How much length of that do you have room for?
Spectra and kevlar are lighter than steel cable, but not much smaller for a given strength.
The Futuristic advantage for this would be a "carbon-nanotube" cable, not yet invented,
which you may boldly presume requires 4-10 times less cross-section than steel.
In TOW missiles (Tube-launched, Optically tracked, Wire-guided tank-killers),
the wire is coiled inside the rocket-propelled projectile, freely unwinding rearwards as the missile flies.
This eliminates problems of yanking mile-long cables at hundreds of MPH's through the air.
But it's extremely thin wire, no strength.
Sounds to me like you wish to ascribe magic properties to your game's grappling hook.
One more thing: realistically, the grappling hook's attachment point on the airplane is a problem.
Planes are not built with weight-bearing points all over.
The deck hook under a carrier-landing aircraft must be hung from a strong spine the goes forward into the body.
Seems to me hook would bounce off instead of hooking,
and if it hooked, planes are built light enough that it would likely tear away.
It's almost a crude non-explosive projectile which would damage the plane randomly but not capture it.
In many cases of long cables the initial shock of becoming taught is softened by the elasticity.
And of course the airplane is travelling mostly orthogonal to the reach of the cable,
which slows down the tightening abruptness much more.
Then the tank might be lifted some if the centripetal force plus the maximum lift of the wings
is more than the weight of the tank (you may do the math), otherwise the airplane will arc down and crash,
or the hook will tear out doing random degrees of damage.
If the plane arced all the way down to a crash, the tank might slide a little at the end of the arc.
Not much, really. Sliding is almost as hard to do as lifting.
If the hook grabbed on late, the plane's non-orthogonal vector would pull the cable taught more abruptly,
and either snap the cable or tear away from the plane.
If the hook flew across the plane's path ahead of the plane,
the plane might run into or snag the cable somewhere.
It's noticeably easier to intercept a line than a point.
This might slip off but also throw the plane out of control, recoverably or otherwise.
Cable is likely to be cut, too, and/or cut into part of a wing.
The one thing I'd neglect is the tank breaking. Cable breaking is a penalty,
and similar in game-effect to breaking the winch.
I also seem to be forgetting the plane's thrust.
Just a little hard to imagine it can be appropriately directed against the cable's pull.
But I should not be entirely sure.
I think this is a wildcard move that should almost never do a predictable thing,
even with a perfectly self-guided barbed spear.
Could waste a lot of HPU cycles. (Human Programmer Unit)
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Update: June 2012