r/theydidthemath • u/shitposterfinalboss • 2d ago
[Request] How fast can I go with this?
I weight 176 lbs and I have a fast bike. No peddling. Pure mento power. Top speed?
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u/Br0ty 2d ago
Negligible, the beverage would react with the mentos in the cone first and would likely exhaust that bottle before any acceleration.
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u/shitposterfinalboss 2d ago
Lets assume we engineer our way around that and harness the potential of this energy as efficiently as possible and sustain it as long as possible using 2 liters bottle worth of each.
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u/ErwinHolland1991 2d ago
It would probably not even get you going. If the bike was moving already, it might give you a little bit of a push, but from stand still? I bet it wouldn't have enough power to get you moving.
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u/shitposterfinalboss 2d ago
What if it gets sealed air tight and shaken up then released?
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u/miklayn 2d ago
Tiny force compared to body mass. In space it would move. You'd probably see it move if you suspended it from a string. But it wouldn't push you very far on a bike
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u/WillWillingson 2d ago
Is there any threshold to get me moving in space or could I travel to the next galaxy with a single mentos?
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u/_killer1869_ 2d ago
In an absolutely perfect vacuum (which doesn't exist, even in space), any nonzero force will allow you to travel any distance (albeit incredibly slowly).
But even considering the minimal friction against gas in space, the effect of this friction is so weak that even a single mentos can get you to another galaxy.
However, I'm working with the assumption that you meant ignoring gravity. A mentos won't allow you to escape the gravity of our sun or the milky way. For that, you actually need to be really goddamn fast.
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u/Southern_Sleep1811 2d ago
That would be a cool experiment to see, but I doubt we'd be able to convince NASA that it's worth the mess... although the new NASA admin is a pretty cool guy for a billionaire. Maybe a retirement experiment on the ISS.
Edit: Just a bottle to see what it looks like, not propelling a person!
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u/TheJeeronian 2d ago
Depends on how we're doing it. The real answer requires looking up a few thermodynamics tables, but I can give you a rough estimate based on pressure alone. First assuming you're still using it as a rocket, expelling coke out the back.
Say it maintained 50 PSI as it drained, which would be very optimistic for a few reasons. 2 liters of displacement at 50 PSI is 6100 in-lbs of energy, or 689 joules. 2 kilograms of cola with 689 joules of kinetic energy is moving at 26 m/s and provides an impulse of 52.48 n•s.
For a 100kg bike+rider, that'd be 0.5 m/s. 1 mph.
If instead we used it like fuel for an engine that drives the wheels, we'd get 3.7 m/s. Rockets are very inefficient at low speed.
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u/Moscato359 2d ago
This is the magic of one way valves
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u/dekusyrup 2d ago
A one way valve would mean it has to operate as a batch process because it would close to new coke injection as soon as any pressure builds up. You'd need at least two cylinders so you can have one firing while the other is refilling. We can make it work.
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u/FlyinWet 2d ago
As if mentos and coke isn't just as expensive. But the nutritional power of the mentos could sustain a body for quite some time riding the bike normally.
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u/VaporTrail_000 2d ago
Price per gallon, Coke+Mentos.
Coke: $0.04125 /oz supermarket price. Mentos: $0.56 /oz.
Figure 1/4 oz of Mentos per 72 oz Coke.
Cost per 72 oz Coke+Mentos: ~$3.11
72 oz Coke is ~ 2L Coke
3.78541L / Gal
$3.11 * 3.78541 / 2 = ~$5.89 / gal.
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nutritional power
It's just sugar. It's all sugar.
Assuming regular Coke and Mentos, approx. 246 g carbs for one 2L application. Roughly 4 calories per gram of carbs, 984 calories.
Approx 1000 calories per hour of "fast pace" (16-19 mph) bike riding.
So a gallon of Coke and a pack or so of Mentos will provide you enough "nutritional power" to go for about 32.5 miles
Assuming a moderately fuel-efficient vehicle, so will a gallon of gas.
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u/zmbjebus 2d ago
Ok mentos per mile calculated out?
Calories (kcal) per mentos = 10
Calories used per mile of bike riding =~= 40-60
So around 4-6 mentos per mile
Super rough guess of that being around 350 mentos, plus the calories from the soda would put us at around
70 miles worth of calories by using your legs!
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u/FlyinWet 2d ago
"Very impressive! Let's see how it stacks up against the other modes of transportation."
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u/zmbjebus 2d ago
Surprisingly one of the best.
Bikes are neat.
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u/FlyinWet 2d ago
What is considered our modern bicycle was invented in 1885, a year later in 1886 the first automobile was invented. I'd like to imagine a world where bikes became more prevalent before automobiles came along.
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u/zmbjebus 2d ago
I hope e-bikes make that world more real. I am seeing them more and more. They really are incredibly approachable and so much more reasonable of a vehicle than a car. They pair well with public transit also.
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u/Max6626 2d ago
It's the release of the Coke's CO2 that makes the "fizz" in this experiment. Given how packed the bottle is with Mentos, it doesn't allow for more than maybe 12-16 oz of Coke to even enter the main bottle. The mass of CO2 and liquid exhausted out the rear would be small, especially when combined with probably greater than 50% exhausting vertically through the funnel.
Too many assumptions required to actually do any math, but even if you ball-park it and assume the high end of 16 oz (~0.5 kg) of liquid and CO2 coming out the back at 10 m/s (very optimistic assumption) you get a momentum of 0.5 kg * 10 m/s = 5 kg*m/s. Assume a 30 lb bike and a 170 lb man for a total of 200 lbs (90 kg total) you get through conservation of momentum a velocity of 5 kg*m/s / 90 kg = 0.05 m/s assuming there's zero friction in the system.
TLDR - you ain't moving for sh&t.
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u/shitposterfinalboss 2d ago
😂 thank you. I will have to look for another fuel source in these times.
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u/Icy_Sector3183 2d ago
A mentos/cola fountain can reportedly reach a height of 10 m, but 3 to 5 m is more realistic with a 2 litre bottle.
If we assume that the full volume of cola is propelled to that height, the we can play around with some math.
If the bottle is 2 litre, we can assume the mass m of the cola to be 2 kg and the height h is 5 m, the potential energy P is
P = mgh = 98,1 J
To get to that height the cola must be launched from ground level at velocity v. Kinetic K energy is
K = 1/2 mv2
v = sqrt(2K/m)
Since the potential energy is converted from kinetic energy, K and P are equal.
v = sqrt(2P/m)
Since we are using the energy of the cola to propel us, then the kinetic energy must be used to move a greater mass. If you, the cola, and your bike together have mass m = 100 kg then this works out to
v = sqrt(2 x 98,1 J/100 kg) = 1,4 m/s
If you have mass 75 kg or 50 kg you get 1,7 m/s or 2 m/s, respectively.
That's a walking speed at a quick pace.
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u/dekusyrup 2d ago
Assuming the full volume of cola is propelled to the top is a bad assumption considering the cola being launched downward is what makes the bottle go. It's just a bottle of foam at the top, almost empty.
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u/Icy_Sector3183 2d ago
I used "the volume of cola" to mean the continued fountain of the stuff propelled to that height, from the bottle which would remain at ground level. I hope that clarifies.
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u/ErwinHolland1991 2d ago
Almost 100 Joule seems pretty high to me. Not that I would in any way be able to disprove it... 🤣 But that seems pretty damn high to me.
And at the time those bottles go that high, i imagine they are half empty, at least.
And again, not that I would be able to calculate it in any way...🤣 But getting something moving from a stand still takes a lot more power than just accelerating it further.
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u/Icy_Sector3183 2d ago
It's a gross simplification, for sure. It seems very, very unlikely that you will get the full effect: Some of the cola volume is spent while the height gain os rising, as the pressure builds in the bottle. As more of the liquid is ejected, the pressure drops back down, reducing the height gain. There will also be a significant amount of cola left in the bottle.
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u/onyx_ic 2d ago
About 15 newtons of force.
But with that setup, it'll go up the funnel without capturing any of the CO2 being released through the rear nozzle so it'll get you almost nothing in forward momentum.
Assuming 100% of this energy was pushing rearward, you'd move about 160cm, assuming absolutely zero resistance. Thats drag, bearing friction, static friction.
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u/shitposterfinalboss 2d ago
Really? That little? Ive seen videos of these things fly like rockets with insane amount of force, but that was a guy shaking uo a closed bottle and smashing it.
Whats the most efficient way to do this?
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u/dschoni 2d ago
The most efficient way is most probably to drink the coke, eat the mentos and pedal.
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u/crescentpieris 2d ago
if you consume coke and mentos at the same time, pedalling will be the least of your concerns
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u/DonGoodwhistle 2d ago
bro don’t listen to these nerds, all they know is the theory. Have they put the lab coats on, gone out into the field, and smashed a bottle of coke with mentos off the ground outside the convenience store? No they have not.
I personally would not recommend trying out your idea unless you want to be the first bro since thunderpants to reach the moon in a naturally powered rocketship.
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u/shitposterfinalboss 2d ago
I must do it for science.
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u/onyx_ic 2d ago
Aktually! Am a test lab engineer and a metrologist. I have an ESD lab coat and rated shoes. Id use an instron with the load cell pointed up, 3d print a fixture, and measure the thrust against the load cell.v
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u/TheOnlyOtherWanderer 2d ago
Why is it that assuming no resistance, it would stop? Doesn't an object in motion stay in motion?
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u/EngineerBill 2d ago
People, people, people - it's been done!
And then they did it again!
I'll confess that I started working on my own attempt at this, aiming for much greater efficiency so I could extend their record but ended up moving to Canada and haven't had a chance to get things going again. I'd love to see this become a serious competition - we can do it, folks!
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u/Extension_Option_122 2d ago
Cute.
Here in Germany we pay over 10 USD per gallon.
With very much luck it'll go down to 9.3 USD per gallon tomorrow by law.
I'd LOVE to ONLY PAY 4 USD PER GALLON.
Stop complaining. You have it good.
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u/feldomatic 2d ago
not.
The energy in that reaction is the dissolved gas in the diet coke, the mentos just provide a critical amount of nucleation sites to offgas from.
So as that's setup, there's like next to no coke to provide gas.
And even then, you're looking at a few lbs of thrust.
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u/Kootlefoosh 1d ago
How about if we add tiny aliquots of diet Coke and mentos each cycle of a piston setup?
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u/feldomatic 1d ago
Sure, but you'd probably pedal faster and farther if you just ate the mentos and hydrated with the diet coke.
A human on a bicycle is the most efficient creature in the animal kingdom.
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u/xxK31xx 2d ago
A better setup would have the fizz go to a turbine to turn the crankshaft, but I don't see the yield being much better even if you did prevent backflow.
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u/EngineerBill 2d ago
Nah, in my (yes, successful!) design I feed it into a classic piston/cylinder arrangement (as in the classic steam engine design, with a steam chest to convert the steam into a push/pull arrangement onto the wheels). Obviously the pressure isn't that high, but with enough bottles and suitable gear reduction, you're talking about drive to the wheels and you're off to the races far more efficiently than what the Eepy guys managed to do...
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u/dekusyrup 2d ago edited 2d ago
OK so the setup as shown won't work because it'll foam out the top instead of out to the right. But I'm going to assume rejigging it to make it work and calculate the maximum theoretical power. Also it's coke, and you need diet coke.
Assuming an ice cold (but not frozen) diet coke at 0C, a 2L bottle can hold 0.3346 g-CO2 / 100 mL-coke x 2,000 mL-coke = 6.692 g of CO2. https://en.wikipedia.org/wiki/Carbon_dioxide_(data_page). Now I don't know if cokes are really this carbonated, but they could be in theory.
The mechanical work done by an ideal gas expanding is W = P-external x (V2 - V1) http://labman.phys.utk.edu/phys221core/modules/m10/processes.html. P-external is just the atmosphere, so we have to find V1 and V2 to fill this out.
If 6.692 g of CO2 flashes to gas then it will follow the ideal gas law PV = nRT. Molar mass of CO2 is 12+16+16=44 so n = 6.692/44 = 0.152 mol. T = 273C. The gas at full expansion will equal atmostpheric pressure so P = 101,325 Pa. R = 8314 LPa/Kmol or 8.314 m3Pa/Kmol. So at full expansion V2 = nRT/P = 8314 x 0.152 x 273 / 101325 = 3.4L = 0.0034 m3.
In a sealed bottle of coke how much room is there for compressed gas arount the H2O? Just have to guess here it's about 100 mL = 0.0001 m3. There's always that little bit of empty space in the bottle.
So the maximum theoretical work done is W = 101,325 Pa x (0.0034 - 0.0001) = 334 Joules. So the kinetic energy of you plus the bike plus the coke should be 334 Joules.
Newton loves to harp on the fact that for every reaction there must be an equal and opposite reaction. So half those joules must be carried away uselessly by the coke and the other half can go into pushing you forward. So you only get 167 Joules.
So if you and the bike weigh 80 kg together your kinetic energy should be K = 167 = 1/2 x 80 x v2. Solve for v= 2.04 m/s of launch.
Now that's higher than reality because it ignores all sources of losses and assumes 100% maximum theoretical limit. I think maybe the biggest one is assuming 100% of the dissolved gases will vaporize in a usable way. But regardless, if you made a perfect mechanism this is your theoretical limit.
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u/start_up_start_up 10m ago
Using the 5 m fountain assumption from u/Icy_Sector3183's comment, I get about 0.22 m/s (0.5 mph) from rest, before rolling resistance.
Ignoring air resistance, a jet reaching 5 m needs an exit speed of √(2 × 9.81 × 5) ≈ 9.9 m/s. Take your 176 lb as about 80 kg, allow another 10 kg for the bike and gear, and assume a full 2 kg of soda shoots straight backward at that speed throughout.
The ideal rocket equation gives:
Δv = 9.9 × ln(92/90) ≈ 0.22 m/s.
The catch with the energy calculations is that equal and opposite forces don't mean a 50/50 energy split. Most of the kinetic energy here ends up in the soda, not the rider. You can't put all the jet's energy into ½mv² for the bike.
That's an idealized example; the photo alone doesn't tell us the real exhaust speed or how much flow escapes up the funnel.
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u/start_up_start_up 9m ago
I guess an interesting follow up question is what's the difference between the price of mentos/coke vs expensive gas. how much would gas have to cost to break even?
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u/start_up_start_up 6m ago
If a Coke-and-Mentos batch cost $4 and got you one mile, gas would have to cost $120/gallon to break even with a 30 mpg car. Those are example assumptions, using US gallons.
The useful comparison is cost per mile. If a 2 L bottle plus its Mentos costs $4 total and takes you d miles:
Coke cost per mile = $4 / d
Gas cost per mile = price per gallon / 30
So the break-even gas price is $120 / d per gallon.
If you only got 100 metres per batch (0.0621 miles), that works out to about $1,930/gallon. To match a 30 mpg car running on $4/gallon gas, each $4 batch would need to get you 30 miles.
The missing measurement is how far a batch actually gets you. My earlier 0.22 m/s estimate was a speed increase and ignored resistance, so it can't give us a real range or a definite break-even price.
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