So, here’s the breakdown of the scene from last night’s episode. You’ve got a red shirt on top of an 800 foot tall, 20 ish foot wide wall. A giant at the bottom of the wall, about 15 feet away, fires a 10 foot long arrow at the red shirt. The red shirt gets hit by the arrow, launched in the air to the other side of the wall and down the other side.
The questions:
Assume the arrow is roughly 10 pounds, the red shirt is 150 pounds, and all the momentum from the arrow gets transferred to him. How fast would the arrow need to be going to knock him 20 feet? (It’s unclear how high in the air he gets sent, but it’s at a fairly steep angle.)
If the arrow was going said speed at the top of the 800 foot wall, how fast was it going when it left the bow? And how much force would be required to launch it?
For a projectile capable of lifting a man off the ground, 100 fps is slooooow.
Most modern bows are advertised as shooting somewhere around the 300 fps mark. In practice, they’re usually more like 270-280 fps.
On a review of the play, it appears to me that the arrow’s flight is about one second. The Wall is reputedly 700 feet high. 700 fps puts it on par with a very slow bullet. This is just a guesstimate, though. Youtube doesn’t time to the millisecond, we assume there was no time lost when the shot cut, and we can’t calculate the hypotenuse without knowing how far the giant was from the wall.
I’ve wasted a little time on this so far this morning.
The Giant was aiming pretty vertically. If he was 30’ from the wall, the effective distance is still pretty much 700’. We can call it 701 or 702 if you want.
The time - assuming that the scene wasn’t cut was 1.06 seconds. That’s me frame by framing it.
Now, to get from the giant to the wall in 1.06 seconds, you’d need (assuming that the pull of gravity is the same in Westeros as it is on earth) the arrow to leave the bow at 224 m/s. That’s fast - especially when you consider the projectile.
Lots of assuming here - but I’m only going off whats shown on the show. When the giant walks up, you can see that the arrow is much longer than the man standing next to him. 10’ is probably a pretty good guess. When the guard kabob hits the ground, the arrow looks to be about 2" in diameter.
Assuming that the wood the giant used was similar to ash here on earth, we’re looking at an 8.79lb projectile.
I haven’t calculated the force yet - but if the giant were able to move an object that big, that fast, it would easily send a man flying.
If we assume 700 fps and ten pounds, then we can estimate with a pretty simple math problem:
Momentum = mass * velocity. So the arrow had a momentum of 7000 foot-pounds per second. Let’s assume the target is 150 lbs. Assuming all of the momentum is transfered (which it wouldn’t be, but most of it might), his new velocity after he is struck is 7000/150, which is about 47 fps. That’s pretty fast, and therfore at least somewhat plausible that it might send them flying. As to the arc he would then ‘fly’ at, that would depend on the angle at which he is struck and would involve a bit more complicated math.
I think the real question ends up being whether or not you could transfer 7000 ft-lbs/s of mometnum from an arrow traveling at 700 ft/s to a man over the course of the arrow’s 10’ of length.
My money is on the arrow passing through the guy and leaving him on the wall. Well, most of him, anyway.
It should leave the bow at about 900 fps, it needs to hit the man at about 120 fps.
If you raise a 10# arrow 800 ft it will be storing about 8,000ft# of kinetic energy
If a man is running at 19 mph and leaves the ground he will travel about 20 ft requiring about 1800 ft# of energy.
Not counting drag on the arrow it would require about 10,000# of energy, allowing about 20% for drag this would put him at about 12,000# of energy.
a 10# arrow traveling at 900 fps will be carrying about 12,000 of energy.
Yeah, what was the giant using for an arrowhead, a brick? I used to bow hunt and have shot completely through a deer with a 80lb pull compound bow. It ran about 20 yards and fell on it’s face dead. The force of impact imparted from the arrow didn’t even seem to bother the deer.
Hollywood physics. Just like when someone gets shot and the force blows the dude across the room, no that doesn’t happen either.
Stand still, this is gonna sting a bit, but its all in the name of science.
I will double check when I get to work but if that is a forged iron arrowhead, that might easily add another 4-6 pounds. That might skew some the calcs toward a more reasonable non hypersonic launch speed.
Squirrels have been shot with target tips and the skin pushed right through the squirrel without breaking the skin thus knocking the squirrel for a loop and killing him of course. If the tip of the arrow could not penetrate the armor then he could be knocked for a loop.
It would be more plausible if the arrow didn’t penetrate him, just knocked him back and he landed on an unrelated spike on the ground
although if he had fat armour, and if the flooring and stuff he was on also got hit and helped the arrow not cut through but launch him it would be more plausible
