Question for engineery b3tans
I'm having an arguement with someone on YouTube (yes, I know) about how fast the Saturn V rockets were travelling when the tail cleared the top of the tower. Based on the rocket taking 12 seconds to clear the distance (info taken from NASA website) and having a length of 110m, this gives an average acceleration of 18.3ms^-2 and a speed of 63.45ms^-1, or 142mph after 110m - NOT 40mph like this guy is claiming (I think his maths and reasoning are rather dodgy). It's a bit more reasonable than the 300mph+ I claimed at first, but that was based on an overall acceleration for the rocket during first stage flight as a whole. I suspect I'm going to have to do thrust calculations next...

Would someone nice please be able to check my maths and tell me if I'm talking bollocks or not?

Linky to the vid
(Potty Jag har smör i min rumpspringa, Tue 30 Jun 2009, 10:32, 21 replies, latest was 17 years ago)

Looks about right to me...
...I'd be amazed if the Saturn was moving as slowly as 40mph after 110 meters of flight given the in-capsule footage of the effects of G on the astronauts.

Remember that a decent 100 metre runner will have a velocity of circa 30mph by the time they cross the tape.
(Bicycle Repairman "you're also a bit of a wanker", Tue 30 Jun 2009, 10:43, Reply)

Well
Using the standard equations of motion, s=0.5at². So a=2s/t². Therefore if s=110m and t=12s, a=1.52ms^-2.

And if v=at, then v=18.3ms^-1

which is about 40mph.

Although intuitively you'd expect the acceleration and hence the velocity to be a bit more than that.
( K2k6 has a proper job these days, Tue 30 Jun 2009, 10:46, Reply)

Thanks K2!
I don't doubt your maths, but I do doubt my own intuition now!
(Bicycle Repairman "you're also a bit of a wanker", Tue 30 Jun 2009, 10:48, Reply)

This makes more sense now I see it
Going to have to double check my maths now and get back to you. Always willing to be proved wrong.
(Potty Jag har smör i min rumpspringa, Tue 30 Jun 2009, 10:50, Reply)

damn you
took me longer to decide whether to type it up or not!
( Vipros. clever got me this far, then tricky got me in, Tue 30 Jun 2009, 10:51, Reply)

It's actually 40.938mph
using 5280'/mile and 1m=3.281 feet.
(Herr Doktor Lemminge Is bored, so cheer me up!, Tue 30 Jun 2009, 11:08, Reply)

Given the errors in the length of the tower
and the time, 40mph is close enough!
( K2k6 has a proper job these days, Tue 30 Jun 2009, 11:10, Reply)

Yeah
Surely we can get more precise data though.

And I just converted your answer into mph.
(Herr Doktor Lemminge Is bored, so cheer me up!, Tue 30 Jun 2009, 11:16, Reply)

Nope
Sure Nasa sent men to the moon but the only guys that could operate a tape measure were drunk...always.
( Captain V, Tue 30 Jun 2009, 11:17, Reply)

Well if half the stuff about NASA is true
This fact doesn't phase me in the slightest!
(Herr Doktor Lemminge Is bored, so cheer me up!, Tue 30 Jun 2009, 11:49, Reply)

Thing is,
rockets don't have constant acceleration do they?

They provide constant thrust (ish) but their mass changes.
(Shippy likes linebreaks and doesn't care what you think, Tue 30 Jun 2009, 11:42, Reply)

but over a short period
you can assume a constant average acceleration without too much trouble
( Vipros. clever got me this far, then tricky got me in, Tue 30 Jun 2009, 11:49, Reply)

Well
if you're going to be making assumptions... ;)
(Shippy likes linebreaks and doesn't care what you think, Tue 30 Jun 2009, 11:54, Reply)

I'm an engineer
that's what we do
( Vipros. clever got me this far, then tricky got me in, Tue 30 Jun 2009, 11:59, Reply)

I've done the maths
and I come out with 40 mph too, which seems wrong to me

using equations of motion v = u + at gives v = 12a
s = ut + 1/2at^2 gives s = 72a or a = 110/72 = 1.5 m/s^2 and v = 18.3m/s

doesn't seem right though
( Vipros. clever got me this far, then tricky got me in, Tue 30 Jun 2009, 10:51, Reply)

Wow!
I quite like being proved wrong... Thanks guys!

I always assumed that the footage used in the famous launch tower shots (also seen in Apollo 13) was slowed down. I guess I was wrong there too.
(Bicycle Repairman "you're also a bit of a wanker", Tue 30 Jun 2009, 10:55, Reply)

it's weird isn't it
but then you've got to figure it weighs a shitload.

thrust is apparently somewhere in the region of 35 MN (Mega Newtons) which is an awful lot, but doesn't result in massive acceleration right off
( Vipros. clever got me this far, then tricky got me in, Tue 30 Jun 2009, 10:59, Reply)

What you have to remember about rockets
is that they weigh a hell of a lot on launch, and the majority of it is due to the mass of fuel. So as the fuel burns off, the thrust, which remains essentially constant throughout, causes the acceleration to increase.

Once most of the fuel has burned off, the rocket's a fraction of its launch mass and hence the acceleration is several g.
( K2k6 has a proper job these days, Tue 30 Jun 2009, 11:08, Reply)

This is the mistake I made when I originally did the calculation
Came out somewhere in the region of 300mph as I hadn't factored in the mass of it at launch and did a calculation based on the final speed at the end of the first stage, forgetting that the acceleration would keep rising. I've redone my figures though and I can see where I went wrong with this - will try to remember if I have to sue them in the future.
(Potty Jag har smör i min rumpspringa, Tue 30 Jun 2009, 11:17, Reply)

Yes - makes sense
I know that the shuttle dumps the equivalent of an olympic sized swimming pool in a very short time on takeoff.
(Bicycle Repairman "you're also a bit of a wanker", Tue 30 Jun 2009, 11:20, Reply)

thrust
He does say it builds up to 7.6 million pounds of thrust. The video shows it takes about 8 - 9 seconds to clear the tower and takes 26 secs to reach a height of half a mile (approx 750m).

Also, the countdown runs slightly faster than the video time. So, I suspect the video has been slowed down slightly unless the guy doing the countdown is just doing it in his head rather than using a large display which I imagine there is at mission control.

Some things to consider.
( sandettie light vessel automatic New Twitter - @bollocksreally, Tue 30 Jun 2009, 14:10, Reply)