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Sonic's Top Speed on the Genesis - The Physics of Sonic

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Posted

 

 

dist2 = 2742.5 m2; dist = 52.4 m

So, the conservation of energy equation now looks like:

0.5*v_i2 = 0.5*80.9 + 9.8*7.7 + 0.4*24.5*59.3

 

v_i2 = 2*(40.5+75.5+581.1) = 1394.2

v_i = 37.3 m/s

 

Whoops! I used the wrong distance in the final equation! Let's try that again:

0.5*v_i2 = 0.5*80.9 + 9.8*7.7 + 0.4*24.5*52.4

v_i2 = 2*(40.5+75.5+513.5) = 1259.0 

v_i = 35.5 m/s

 

This is the same as 79.4 mph or 127.8 km/h. The maximum speed of a cheetah is 120 km/h (from Wikipedia, but heavily backed up by citation). So, even if Sonic isn't capable of supersonic speed based on my calculations, by the time Sonic 3 came out, Sonic really was the fastest thing alive (on land)! Still, I look forward to seeing how fast you can get Sonic to go!

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Posted

Although I flunked Physics I'm glad I understood most of that, shows 2 years wasn't in vain!!

Would a good test be to try and determine his speed on a loop?

He would have to go upside down and we have sonics weight and height, surely we could measure the diameter of the loop using "sonics"?

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Posted

I tried to do calculations on the Green Hill Zone loop and came up with something uninspiring like 8 m/s... 
However, if you want to use a different loop, look for a very large one. The higher and higher you go, the more potential energy you have, so you need more kinetic energy and therefore more speed at the bottom to do it.

Also, like I said, for circular motion, a = v2/r, and at the top of the loop, a will always equal g, or 9.8 m/s2.

so, the speed at the top of the loop equal the square root of the radius and 9.8 m/s2. The greater the radius, the greater the speed must be. 

Overall, then, if you want to use a loop, use a very big and especially a very tall loop to do it.

You can also try looking for a maximum speed on the 3D games if you can outdo the Game Theory figure of 80 m/s. Again, good luck!

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Posted

The last thing would be to determine how fast he is moving on order to run into of the water in Hydrocity?

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Posted

The ability to run on water has less to do with how fast you're traveling and more to do with how much force per area Sonic's feet press down on the water. He has to have quick feet to achieve this, therefore. At 20 degrees Celsius, the surface tension of water is 0.0728 N/m, if that's any help.

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Posted

Having to have quick feet by extension would show how fast his feet was moving, maybe we could work out from there the speed of his movement?

Like using the distance of his stride would be the distance he moved per footstep, and if he has to say for example move his feet 100 times a second to stay on top of the water then we would times that by the distance of his stride, say 0.5m, to get the minimum speed? In the example case this would be 50m/s?

Of course that was all rough but would that be along the right lines?

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Posted (edited)

Super Sonic or does he have to be in regular form and on the ground? Because was thinking what about the Doomsday zone than. If not try adding the speed shoes. Try putting Sonic in Mario world and multiply how many times faster he is than Mario. Okay Good luck frying mind in!

Edited by TailsTellsTales

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Posted

I didn't think about measuring Sonic's stride; that's a really good idea! It will allow us to relate the speed of Sonic's feet (which is important for surface tension) to speed (which, of course, is what we're trying to determine).

So yeah, Jolt, all of that sounds like it would work really well! I'm a little too busy at the moment to try it myself, so go ahead and see if you can do it. If you're busy, too, or just don't want to do it, I can try tackling it in about a week or so.

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Posted

I'll give it a go, but I only up to did A-level physics :P

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Posted

Physics aside (yeah I never made it that far in HS... I suck at math...) from a programming point of view the only reason why Sonic wasn't as fast in the first Sonic game is due to a speed cap that was programmed in. Yuji Naka would get motion sickness as the rumor goes, so he is probably the one that programmed that into the first two games. (The second game got rid of it when Sonic's on the ground, but it's still present while he's in the air...) In Sonic 3 they completely got rid of that "feature". The guy who uploaded that video probably didn't know or did know but failed to mention that little fact from the first two Sonic games. Still it's great to see the amount of knowledge you have put behind this theory. smile.png

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