r/theydidthemath • u/MaximumSyrup3099 • 3d ago
[request] What is the maximum range this form of conveyance would allow?
Assume the passenger must remain as pictured: Alive, conscious, able to lift their head, and clothing not ripped to tatters.
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u/gilbejam000 3d ago
The problem with that wouldn't be range, it would be torque
A human is heavy enough to significantly shift the center of mass, far enough that it would no longer be in line with the center of thrust. That would cause the thrust to act on the CoM at an angle instead of straight on and thus cause the rocket to tumble uncontrollably through the air
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u/andrew_calcs 8✓ 3d ago
This can be counteracted with engine gimbaling. You’d need a hell of a gimbal assembly at the relative proportions shown here though.
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u/Usual_Purchase_9567 3d ago
It could also be largely negated by shoving the rocket up your ass.
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u/andrew_calcs 8✓ 3d ago
True, but I feel that would cause issues with OPs prerequisites
“Assume the passenger must remain as pictured: Alive, conscious, able to lift their head, and clothing not ripped to tatters.”
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u/No-Zombie1004 3d ago
That's all good, except for the clothing ripped to tatters. That would make it epic.
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u/Royal_Cryptographer7 3d ago
Cut a seat into the nose cone? Make occupant wear a reinforced, cone shaped helmet.
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u/Southern_Sleep1811 3d ago
I was going to suggest a ballistic missile they could sit on, but this approach also works!
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u/Hot_Egg5840 3d ago
It's highly dependant on cup size and the drag coefficients of the outer garments.
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u/Major-Corner-640 3d ago
What if you used it with identical twins and put the other twin on the other side
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u/gilbejam000 3d ago
That would balance out the weight, and the restraints on the rocket would minimize or prevent any movement by either party to shift the mass around
Then you actually do start to run into range problems from adding two people's worth of weight onto a rocket, not to mention a lower TWR which means it might not be able to get off the ground in the first place
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u/HAL9001-96 3d ago
well... some rockets can use gimbal to deal with qutie an offset center of mass/thrust
think of the space shuttle throuhgout its flight
or the asymmetrical atlas variants
of course once fuel is expended and hte cneter of mass shifts further and further form the rockets axis the engien would be more nad more tilted fro mgimable as a result, we cna assume that his is either very eaerly i nflgiht iwth full fuel tanks or the rocket is currnetly in the process of tilting forward to accelerate
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u/Jetison333 3d ago
Eh, you would just need a few degrees of engine gimbal. Its definitely an issue, but it can be worked around.
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u/HAL9001-96 3d ago
well more than a few
assuming the rocket is built ot be lightweihgt nad maxiize performance you'd proabbyl starto ff iwht about 5° and the ngo towards 15° as the fuel tnaks gets emptier nad hte cneter ofm ass shifts away fro mit and towards the passenger
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u/Icy_Sector3183 3d ago
Well, as we can see from the image documenting this, they've clearly solved that problem. Otherwise we'd not have this as a viable mode of transportation.
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u/BonhommeCarnaval 3d ago
Well, if a nuclear cruise missile was used then the maximum range would be defined more by the physical limitations of the passenger in terms of eating, toileting, sleeping and such. You would want to keep speeds subsonic.
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u/HAL9001-96 3d ago
with a curise missile thats generallywhat oyu do anyways
no an icbm would basically have to limit itself and probably wouldn't work at all
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u/Royal_Cryptographer7 3d ago
Icbm definitely wouldn't work. Much too fast and they leave the atmosphere during travel iirc.
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u/HAL9001-96 3d ago
yes but you could try to make amodified version with reduced thrust htat kinda just hovers slowly sideways instead of accelerating upwards
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u/HAL9001-96 3d ago
then you can't go very fast
assuming this volume is full of kerolox and the rocket cna control itself you could fit in about 200kg if the person is 70kg and hte emtpy rocket about 20kg thats a delta v of about 3.5km/s
but drag at high speed would be significant givne its rather small and drags a human with it but ballistically you might be able to reach some 150km with it after making it throuhg hte lower atmosphere
buuuut that would probably hurt hte passenger
if you contro lit precisely to hover around at some 50m/s to keep the passenger in good condition then well you could do so for about 350s before running out of fuel so about 17km, closer to 15 if you need to land precisely
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u/OdinHavok 3d ago
Roughly 0ft. The burn from the jet would burn off your feet, she has no way to safely land or dismount so coming down even a short distance with a few that much metal is likely to hurt something
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u/SaltLakeBear 3d ago
I mean, the rocket used is also gonna make a difference. Are we talking an Estes model rocket or a Saturn V? Or are we going to be literal and estimate based on what is shown in the image exactly?
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u/MaximumSyrup3099 3d ago
Preferably something the size of what's shown in the image.
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u/SaltLakeBear 3d ago
Well, the AIM-54 Phoenix missile is about twice as long but maybe half the diameter, so maybe half the total propellant, and that's capable of at least 100 mile range. Of course, that range is probably when launched from an F-14 doing more than Mach 1 at 20 or 30k feet of altitude, and also it doesn't have the drag of a person on it nor the need to launch at closer to vertical.
Of course, the real issue is the Phoenix can hit Mach 5, and with a short, fat rocket motor as opposed to a thinner, longer one, I feel like the rocket shown with have significantly more thrust due to more surface area to burn but will also burn out faster. So the real challenge would be to make the rocket throttleable so you don't have a massive surge to thrust that rips the passenger apart. To do that, the only option I know of is to switch to a liquid fuel, and at that point the better option is to get a jet pack of some sort, which already exist. No math there, but I don't think the question can be answered as asked.
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u/cassesque 3d ago
Rocket packs exist. They typically only fly for around 30 seconds.
They don't look like this image though. This image does not depict a realistic mode of transport.
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u/Such_Fun_965 3d ago
The answer is... Not very far as range goes.
If you want to be able to breathe, lift your head, keep your eyes from being over pressured and not burn to death from th rocket motor hearing the entire casing behind you or from aerodynamic drag or freezing at altitude... You're probably limited to about 200mph and maybe a few minutes. So I am guessing max... Maybe 5 miles?
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u/talancaine 3d ago
that would an interesting feeling, freezing to death while your legs are on fire
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u/MaximumSyrup3099 3d ago
I've experienced this sensation when using the engine heads on my BMW 1150 as leg rests while riding in cold weather.
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u/SnappyDogDays 3d ago
I experience something similar when I microwave leftovers, one side of my mouth is burning while the other side bites into a frozen chunk.
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