Measuring the speed of a projectile

My school has a vacuum cannon and it fires small table tennis balls. We can only calculate the velocity theoretically because my school does not have any device that is capable of measuring a projectile traveling at around 350 to 400 m/s

I was thinking of using two tin foils and measuring the time interval of opening circuit. (Using a photo resistor would be too slow)
I did some research and I did find some useful resource: http://forum.arduino.cc/index.php/topic,114435.0.html

Please give me some advice on how I should tackle this problem. (Should I just use the method I found?)

Photoresistor would be fine - you have the same delay in detecting at two points, so they cancel out.
interval time = (T2+time_delay) - (T1+time_delay) = T2 +time_delay - T1 - time_delay = T2 - T1.
Also has the benefit of no tin foil impacting the time by slowing down the ball at all.

We can only calculate the velocity theoretically because my school does not have any device that is capable of measuring a projectile traveling at around 350 to 400 m/s

That fast tennis balls - a joke

of measuring a projectile traveling at around 350 to 400 m/s

Mach 1+ ping-pong balls?

Some serious over-estimation there, I think.

you can measure the soundpulse of the cannon firing and the soundpulse when it drops the floor or it hits the wall.
That too will give you two timestamps and a distance.

If you shoot right up in the air you can even determine the velocity of the ball leaving the canon as the ball makes (almost) a perfect parabola.
Gravity will decrease the velocity until it reaches zero

V = V₀ - g x t

V = 0 when it is at the top, => V₀ = g x t

g = 9.80665 (depends on where you live), and t is half the time between firing and the moment it hits earth again.

example:
so if t = 14.35 seconds => 0.5 t = 7.17 => V₀ = g x t = 9.81 x 7.17 = 70.34 m/s

The height the ball would come is 0.5 x g x t² = 0.5 x 9.81 x 7.17² = 252.16 meter (so don't test this indoors

The above calculations do not include drag / friction.

AWOL:

of measuring a projectile traveling at around 350 to 400 m/s

Mach 1+ ping-pong balls?

Some serious over-estimation there, I think.

It is a 2 meters long vacuum cannon.
P = Atmospherics pressure = 101325 Pascal
r = 0.02 meters
A = (pi)(r)^2

F = PA
F = (101325)(3.14 X 0.04) = 12732.8750
W = Fd = (12732.8750)(2) = 25465.75
W = (1/2)(m)(V)^2

V = square root((2 X 25465.75)/0.04) = 1128
V = 1128 m/s

Considering energy loss, we are just assuming it to be around 350 m/s to 400 m/s
so around 780 mph to 895 mph

Don't be ridiculous.

CrossRoads:
Photoresistor would be fine - you have the same delay in detecting at two points, so they cancel out.
interval time = (T2+time_delay) - (T1+time_delay) = T2 +time_delay - T1 - time_delay = T2 - T1.
Also has the benefit of no tin foil impacting the time by slowing down the ball at all.

I am just worried because I have never used a photoresistor for anything... and the projectile is moving very fast...
Also the photoresistor I have is a crap one (I believe) that just came with SparkFun Arduino starter kit...

Edit:
Based on simple calculation
Assuming it is traveling it at 350 m/s, a large projectile (cylinder shape with hemispheric nose and tail) which is around 6 cm
t = d/v = 0.06/350 = 0.0001714 seconds...
Arduino has 16 million clock cycle which is plenty to get readings but I think the photoresistor is just not that responsive...

Use a photodiode or phototransistor.

(your calculations assume a perfect vacuum on one side of the projectile)

Edit:
Sanity check.
0 - 340ms^-1 implies a steady acceleration of v² /2s = 340² / 4 = 28 900ms^-2 or about 2950g.
Can a ping-pong ball really sustain that?

www.phys.csuchico.edu/~lbuchholtz/Papers/VC_AJP.pdf

The above paper says it could be max 287m/s and 4700g (measured with ping-pong balls and photo gates 125-250m/s typically for 0.5 -2m cannon lengths).

AWOL:
Use a photodiode or phototransistor.

Do you think this Miniature Solar Cell - BPW34 will do the trick?

Datasheet:

Do you think this Miniature Solar Cell - BPW34 will do the trick?

No, I don't think it'll be fast enough

AWOL:

Do you think this Miniature Solar Cell - BPW34 will do the trick?

No, I don't think it'll be fast enough

Oh... I don't know what device to use now...

I do believe I mentioned a photodiode or a phototransistor.
If you google "ballistic computer", you may even find circuits.

I do believe I mentioned a photodiode or a phototransistor.

That's what you need, a photodiode or a phototransistor. I don't know why you want to use something different. They aren't that difficult to find.

Can a ping-pong ball really sustain that?

I have the same impression. If the speed was to be that much, the ping pong ball will probably disintegrate inside the cannon.

It is a 2 meters long vacuum cannon.
P = Atmospherics pressure = 101325 Pascal
r = 0.02 meters
A = (pi)(r)^2

F = PA
F = (101325)(3.14 X 0.04) = 12732.8750
W = Fd = (12732.8750)(2) = 25465.75
W = (1/2)(m)(V)^2

V = square root((2 X 25465.75)/0.04) = 1128
V = 1128 m/s

Redo your calcs, this time square r, F=(101325)(3.14x0.02x0.02)=127.328
W=127.328x2=254.657
V=sqrt((2x254.657)/0.04)=112.83 m/s I think

Tom

Well spotted!

I hope I got it right, it was 10 to 1am here when I did the calc.
Tom

I don't think it is possible to fire a ping pong ball at 300 metres per second.

F = PA
F = (101325)(3.14 X 0.04) = 12732.8750

So the 3.14 x 0.04 which you have there, is supposed to be the cross-sectional area of the bore of the cannon,
calculated by pi * r^2 ?

and r is 0.02 m = 2 cm ?

and r squared is ???