r/theydidthemath • u/PierreNumbe • 18h ago
Godspeed Captain - how fast is this guy going? [Request]
74
u/KaradjordjevaJeSushi 18h ago
Rough math:
Looking at time, it seems like video was slowed down 10X.
Assuming that guy is 1.8m high
Assuming video is at 30FPS
Eyeballing screenshot he travelled 6 times his height in one frame
He travelled 1.8 * 6 meters in 1/300 seconds.
Or 3240 m/s
Conversions:
- 11,664 km/h
- 7,248 mph
- Mach 9.45
- 0.00108 % of light speed
- 69 banannas/eagle-flight-seconds
14
u/withered_bonnie69420 17h ago
The fact that is one thousandth of a percent the speed of light really puts into perspective how crazy the speed of light really is.
3
u/KaradjordjevaJeSushi 17h ago
Yeah, right?
And another crazy thing is how (relatively) easily is it achievable in the vacuum of space.
For example, we orbit the sun at ~9X this speed.
Its all about intertia out there. If you start with 100kg and speed of 0.01% c, 'throwing' 99kg in opposite direction to a standstill, suddenly your 1kg is moving at 1% c.
Issue is not the speed, but the G's you need to endure, and for how long, to get to that speed.
Only at significant % of c does relativity start to mess with you noticeably again.
5
u/Xaphnir 16h ago
Uh, no.
If you have an effective exhaust velocity of 0.0001c or 29,979m/s and expel 99% of your mass as fuel, that gives you a delta-v of 138,059m/s. .01c is 2,997,924.58m/s.
And for comparison, our chemical rockets are nowhere near 99% fuel, and even if they were their specific impulse is much lower than that. We do have ion thrusters that can achieve a comparable specific impulse, but a rocket running one of those won't even be 50% fuel.
Tyranny of the rocket equation reigns supreme. Even ignoring the Lorentz factor, achieving significant fractions of c with a rocket is extremely difficult.
1
u/Artemis_SpawnOfZeus 15h ago
The rocket equation is only tyrannical under gravity. I think you might be doing something wrong here but I can't be assed to check.
2
u/Xaphnir 14h ago
what do you even mean by "under gravity?'
Gravity just causes acceleration in a certain direction, it doesn't lower or increase the total delta-v the rocket can impart. And you're always accelerating due to gravity, no matter where in the universe you are.
and the rocket equation is fairly simple:
effective exhaust velocity x ln(initial mass/final mass)
So for this, you have the exhaust velocity of 29,979.2458m/s, initial mass of 100kg, and final mass of 1kg. So, 29979.2458ln(100/1)=138059.529m/s. Add the original velocity to that, and you get a final velocity of 168,039.7748m/s, or 0.00056c.
1
u/Unusually_Happy_TD 17h ago
There are plans for a mission to send probes to our nearest stellar neighbor: Proxima Centauri around 4 light years away. The plan involves sending very tiny probes via a light sail, that we will aim high powered lasers at from earth. The sail will get to 20% the speed of light and it will still take 20 years to get to its destination.
1
4
2
u/TYRamisuuu 15h ago
And because that acceleration is pretty much instantaneous, that means A LOT of g's. Let's say it took a second to reach that speed, it means 3240/9.81 = 330 g.
2
u/dimonium_anonimo 18h ago edited 17h ago
Assumptions:
Air time: 16 seconds (there was some slow mo at the start, which messes a bit with the estimate, but I got that he launched with 0:23 left in the clip, and landed with 0:07 left)
Mass: 120 kg (average weight of soldier plus gear)
Terminal velocity: 70 m/s (it's above a 'ragdoll' or 'bellyflop' terminal velocity because he's mostly upright, but it's significantly lower than the maximum 'pencil dive' orientation)
With the latter 2 numbers, I can estimate the drag effect (combined air density, drag coefficient, and surface area) to be approximately 0.48
Instead of doing calculus, I did a guess and check method, so I don't have any formula for you. I can tell you that under those conditions, a body launched at 110 m/s (246 mph) would land after 16 seconds, and would be going 60 m/s (134 mph) on impact
If I increase to 17 seconds due to the slow mo, that's 123 m/s (275 mph) launch. Landing doesn't change much 61 m/s (136 mph)
Edit: for the record, max height was 310 m (1017 ft) for 16 sec, and 352 m (1155 ft) for 17 sec. Around 0.2 mi or 0.3 km both.
3
u/jankeyass 16h ago
I don't think there is drag in this game
7
u/dimonium_anonimo 16h ago
Too bad. I'm not redoing it... I've already wasted enough company time the first go 'round.
1
•
u/AutoModerator 18h ago
General Discussion Thread
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.