Close to 1/2 the speed of sound (1116 feet/second).
There’s a company that makes what they call an “Airrow” gun. It’s an air-powered “rifle”, where the hollow, notchless (but fletched and broadheaded) arrow actually slides OVER the inner “barrel”, a long, thin tube (all enclosed in an “outer” barrel which protects the fletching, the weak inner barrel, and provides protection from the broadhead blades.
As I recall from a magazine article, they can supposedly get an easy 500 fps from one, and have seen 700 fps in the upper ranges.
Whether the concept is or can be powerful enough to drive the arrow past the speed of sound, is unknown.
Just out of curiosity I ran some numbers to see how it would look. They weren’t pretty.
If you assume an arrow weighs 5 ounces (based on a poorly recalled memory from long ago), that’s 142g.
Assume you want to get that arrow to about 340 m/s, which is approximately the speed of sound.
Assume your bow can accelerate your arrow over a distance of 1 meter (a very rough number, but easy to calculate.
With: f=ma, d=(1/2)a(t)^2, and v=at,
If you solve for f, you get a required “pull” from your bow of about 7500 lbs. That is, almost four tons. I don’t want to think about trying to hold a bow with this much pull, but I don’t think a thumb tab would be enough to allow you to pull the string back.
Other interesting facts include:
The arrow will spend approximately 0.0015 seconds on the bow after the “trigger” is pulled.
The arrow will hit just short of 24,000 gees as it accelerates.
The arrow would have as much energy as a VW Bug going 11 mph, or a 16 lb bowling ball going 107 mph.
Interesting that somebody should have mentioned flechettes, because with these stats on firing, that’s likely what the arrow would become.
All in theory, anyway…
[nitpick]
Are you sure you did that calculation right? I get an answer about 4 times smaller than yours. Mind you, a one ton pull ain’t no picnic, but still! (I think you must have put the factor of 2 from d = (1/2)*at[sup]2[/sup] in the wrong place.)
[/nitpick]
OK, Don Brown once shot an arrow with a “stick bow” that had a muzzle velocity of 507 feet per second and it traveled 4009 feet. Both records for hand bows.
The footbow record is 6084 feet but I can find no record of the velocity. The crossbow record is 6141 feet but again no record of velocity. (Both the later records are by Harry Drake)
If there were shooting identical arrows in a vacuum, you could guess that the muzzle velocity was 777 feet per second (or so ) with the crossbow. But they weren’t and I’m to lazy to figure out the effect how the slowing down to terminal velocity effects the distance traveled. But arrows are very aerodynamic (especially distance cometition arrows) so the effect would be small, I just don’t know in what direction. Either was, your not really all that close to the speed of sound.
It should be pointed out that a crossbow, if it has a sophisticated enough wince mechanism, can have a much greater pull than a man ever could, even using a footbow. If an arrow is ever going to break the sound barrier, it’ll have to be a crossbow bolt.
You are correct g8rguy, I divided by 2 when I should have multiplied by 2. The actual answer only required about 1850 lbs of pull on the bow. I suppose it makes sence that the physics would seem easy, but I’d mess up the algebra. Next time I double check my math.
On the other hand, with a 7500 lb bow I could get the arrow to mach 2, just before it disintegrated. That would be momentarily impressive anyway…
My father owned an archery shop and was freinds with Tom Jennings (of Jennings Archery who popularized the compound by stealing violating the patent of Allen Archery.) Anyway, the guy was basically an engineer and inventor, not so much an archer though. HE was trying to make a very fast flight bow. some of the problems:
-
limb travel. THe limbs have a lot of wind resistance. YOu have to keep reducing limb travel distance to increase speed past a certain point.
-
String stretch. The more stretch a string has, the more energy it gobbles. Old Dacron is about 10% IIRC slower than Fast Flite string.
-
At a certain point the cables and string have to get pretty thick to handle the force of a very strong pull on a very fast cam. THe bow that Jennings made was a bit dangerous. They loaded it up in teh shooting machine to run an arrow through the chronograph. The cables just snapped. THe little metal doodads that hold onto the string flew off and one lodges deeply into a door jamb.
I imagine that if you cut the arrow down to about 10 grains (the unit used in archery–I don’t know the gram equivalent) got a very thin string, a high pull and super thin limbs, you might do it at a very high pull. But then, it’s not so much of a bow anymore.
Just for the record, Crossbows tend to be slower than longbows on a pount by pound basis because of the shorter draw and therefore the lower amount of potential energy stored. Also, many have the arrow drag across the stock.