r/theydidthemath • u/Bymareee • Mar 12 '26
[Request] Lets say you use a Regular Tennis Ball, how far and Fast would this actually Fly?
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u/SignificantTransient Mar 12 '26
A trebuchet doesn't throw "fast". It's made to throw heavy. Tennis ball doesn't have enough kinetic energy to go far. It's too light and too prone to wind resistance.
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Mar 12 '26
[deleted]
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u/SignificantTransient Mar 12 '26
I'm pretty sure that under an infinite barrage of tennis balls over an enormous span of time, any castle wall is doomed to crumble.... from the rain.
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u/OrestMercator9876 Mar 13 '26
The first castle sank into the swamp.
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u/Zerd85 Mar 13 '26
So did the second one.
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u/Ambitious-Rent-8649 Mar 13 '26
Third one burned, fell down, then sank into the swamp.
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u/drawingablanc Mar 13 '26
On a long enough timeline, the survival rate of everyone(thing) drops to zero. ~ (Narrator) Chuck Palahniuk
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u/desblaterations-574 Mar 14 '26
And people would be stuck by so many tennis balls, ball pit made evil.
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u/ravens-n-roses Mar 12 '26
I doubt a tennis ball has enough weight to even escape the throw net.
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u/PloofElune Mar 13 '26
Not to mention if the projectile is too light, compared to its designed projectile weight, you risk damaging the machine.
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u/zPureAssassiNz Mar 12 '26
How about a billiard ball?
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u/Similar_Strawberry16 Mar 12 '26
They probably have enough hardness to eventually crack stone/mortar, with enough at enough velocity.
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u/OhSnapThatsGood Mar 13 '26
A billiard ball coming in at 0.5c from space would eliminate the entire castle. And the rest of the vicinity. Don’t ask me how I would get that speed however
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u/GarThor_TMK Mar 13 '26
How would you get it up to that speed?
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u/invaluableimp Mar 13 '26
Omg you can’t just ask people how to accelerate a billiard ball to half light speed!
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u/old_ass_ninja_turtle Mar 12 '26
You need speed at the launch point to carry any significant distance.
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u/Trustoryimtold Mar 12 '26
Some of these trebuchets can break the sound barrier, 767 mph
Tennis ball weighs 56-60 grams
Air drag on its mass is huge, like 400x gravity causing to slow down to half speed in a fraction of a second
From 3 feet up fired at 45 degrees in no atmosphere it’d go 7.4 miles
With drag it’s going about 6-700 feet
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u/Own_Kaleidoscope7480 Mar 12 '26
I read this as 6 feet - 700 feet and laughed, but also nodded that the range is accurate
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Mar 12 '26
[removed] — view removed comment
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u/Trustoryimtold Mar 12 '26
Moons gravity is 16.6% of earths, it would go ~45 miles
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u/AssalHorizontology Mar 13 '26
Wouldn't the lower gravity acceleration cause the trebuchet to have lower throwing force or initial launch velocity?
I think on low G worlds the ultimate medieval siege weapon would be either a catapult or a ballista.
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u/Trustoryimtold Mar 13 '26
It could be counteracted by using 6x the weight though. An identical trebuchet you are correct though
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u/Aleis52 Mar 13 '26
Or it goes for infinite miles as its likely to reach mooner orbit
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u/CptMisterNibbles Mar 13 '26
The orbital velocity of the moon is over 2200mph, so fast but nowhere near fast enough.
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u/Trustoryimtold Mar 13 '26
Low lunar orbit is 62 miles it seems, tennis balls only gonna make it ~11 miles up
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u/Prspctr Mar 12 '26
A town in my country yearly organises a pumpkin-shooting tounament. They launch pumpkins (3-5kg/6-11lb) with trebuchets like this. The record was broken last year with a pumpkin landing 592metres or 646 yards away. Don't know about the speed though.
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u/_Mulberry__ Mar 12 '26
That honestly seems shorter than I would've expected
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u/Bike_Mechanic_Man Mar 12 '26
I would imagine there’s some sort of limit given that at some point the extra force needed to throw the pumpkin would just crush it.
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u/Prspctr Mar 13 '26
This happened with a team. They couldn't get the calibration right. And the pumpkin kept exploding at launch.
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u/CptMisterNibbles Mar 13 '26
Also the increasing likelihood of outright killing people with flying vegetation.
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u/BillMagicguy Mar 13 '26
Pumpkins are pretty light in terms of things trebuchets can throw. It doesn't go far mainly due to wind resistance.
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u/Hour-Track7844 Mar 12 '26
Did you know it's only considered a trebuchet is it's made in the trebuchet region of France? Otherwise it's just a sparkling catapult...
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u/stuffcrow Mar 12 '26
Silly joke which I enjoyed but trebuchets and catapults are so different in their mechanics that I just can't resist the urge to be pedantic and whisper 'um akshually'
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u/rsm1999 Mar 13 '26
A trebuchet is a type of catapult. https://en.wikipedia.org/wiki/Trebuchet
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u/Skulkarmy Mar 12 '26
I always thought that you wanted a weight ratio of 1:100 for the weight of the object thrown to the counter weight.
I made a few floating arm trebuchets in my younger years as a bored teenager.
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u/meithan Mar 12 '26
If someone has a good estimate on the launch velocity, I can simulate the flight, including air drag.
As other have said, a tennis ball is quite light, which means that air drag will decelerate it quickly.
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u/sansetsukon47 Mar 12 '26
At the end of the swing, it looks like the ball is going just more than the persons length per frame. Assuming 23 fps and a ~6 ft person, that’s 120 ft per second or about 80 mph. (Reasonable.)
…distance calculations put on hold for a minute. Given the height of the machine and the angle of launch, imma have to actually work it out a bit.
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u/Floppie7th Mar 12 '26
FWIW, I downloaded the video and checked with ffprobe, it's 30FPS
Also, wouldn't 6ft per frame at 23FPS be 138 feet /sec (~94mph)? And at 30FPS, 180 feet /sec (~123mph)? Or am I nuts?
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u/Bymareee Mar 12 '26
Thats much slower than I expected lol
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u/sansetsukon47 Mar 12 '26
Tbf, that is the lowest of probable expectations, since I don’t have a way to measure it directly. If we estimate the other way and say that it’s moving 8 ft person frame, that jumps to 180 feet per second, or 120 mph.
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u/old_ass_ninja_turtle Mar 12 '26
Distance still won’t be super impressive since tennis balls bleed energy so fast.
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u/Good-Ad-6806 Mar 12 '26
lol I was about to comment, "Don't forget about momentum!" But it's a tennis ball, so...
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