Introduction[]
We have always seen some characters attacking on another character and sending him/her/it flying.
This blog serves to find the energy yield from sending a person flying at different speed and across different distances.
Methodology[]
Here an average 2016 Japanese male at 25-29 is picked. Because most anime comes from Japan. Fight me. THE average human (1.684 m; 62 kg) is picked.
The target weighs at 66.82 kg and stands at 1.7185 m.
To make a target fall, the center of gravity is likely falling from roughly half his own height to roughly ground floor.
Height to fall = 1.7185 1.684/2 = 0.85925 0.842 m
By PE to KE formula, mgh = 0.5 m v^2
(9.81 9.80665)(0.85925 0.842) = (0.5) v^2
v = ((2)(9.81 9.80665)(0.85925 0.842))^0.5 = 4.105908547 4.063791161
time to fall to this speed = 4.105908547 4.063791161 / 9.81 9.80665 = 0.418543175 0.414391373 s
Now, the kinetic energy from the yield of an attack should 1-to-1 scale to the target hit who flies at a distance before hitting the ground - in 0.418543175 0.414391373 s.
AP of an attack = Kinetic energy carried by the target = 0.5 x mass x (velocity)^2
(Note: Theoretically, when a person at 1.684 m and 62 kg fell down (even without moving any horizontal distance), he will be hit by the ground at his own potential energy of (62 * 9.80665 * 0.842) = 511.9463566 J. But such effect will be very diminishing as the flying distance increases and I am not taking this into account.)
Tally[]
The table below lists out the energy required to send a person flying at a speed across a distance using the Newtonian energy model.
Here I am only picking values for energy from one punch that yields anywhere not lower than 300 Joules (since that should qualify as a peak human feat to even be notable as an impressive feat. Also, I am excluding values that send objects flying at a range of over 6,371,000 m as that would breach the radius of the Earth, which will as well send people flying to the outer space, and by that time the object will as well be flying at sub-relativistic speed, where messy relativism will kick in.
| Range (m) | Speed (m/s) | Speed (Mach) | Energy (Joules) | Energy (ton TNT) | Tier |
|---|---|---|---|---|---|
| 1.28911151 | 3.110855084 | 0.009069548 | 300 | 7.17017E-08 | Street |
| 2 | 4.826355298 | 0.014071007 | 722.1048694 | 1.72587E-07 | Street |
| 2.071956867 | 5 | 0.014577259 | 775 | 1.85229E-07 | Street |
| 3.190813574 | 7.7 | 0.02244898 | 1837.99 | 4.3929E-07 | Street |
| 4.156345474 | 10.03 | 0.029241983 | 3118.6279 | 7.4537E-07 | Street |
| 5.15088477 | 12.43 | 0.036239067 | 4789.6519 | 1.14475E-06 | Street |
| 6 | 14.47906589 | 0.04221302 | 6498.943824 | 1.55328E-06 | Street |
| 6.509694033 | 15.70904814 | 0.045798974 | 7650 | 1.82839E-06 | Street+ |
| 9.115394908 | 21.99706725 | 0.064131391 | 15000 | 3.58509E-06 | Wall |
| 10 | 24.13177649 | 0.070355033 | 18052.62173 | 4.31468E-06 | Wall |
| 14.2136241 | 34.3 | 0.1 | 36471.19 | 8.71682E-06 | Wall |
| 50 | 120.6588825 | 0.351775167 | 451315.5433 | 0.000107867 | Wall |
| 71.06812052 | 171.5 | 0.5 | 911779.75 | 0.000217921 | Wall |
| 100 | 241.3177649 | 0.703550335 | 1805262.173 | 0.000431468 | Wall |
| 127.9226169 | 308.7 | 0.9 | 2954166.39 | 0.000706063 | Wall |
| 142.136241 | 343 | 1 | 3647119 | 0.000871682 | Wall |
| 156.3498651 | 377.3 | 1.1 | 4413013.99 | 0.001054736 | Wall |
| 240.7971507 | 581.086302 | 1.69412916 | 10467500 | 0.002501793 | Wall+ |
| 340.4165759 | 821.4856722 | 2.39500196 | 20920000 | 0.005 | Small Building |
| 355.3406026 | 857.5 | 2.5 | 22794493.75 | 0.005448015 | Small Building |
| 500 | 1206.588825 | 3.517751675 | 45131554.33 | 0.0107867 | Small Building |
| 710.6812052 | 1715 | 5 | 91177975 | 0.021792059 | Small Building |
| 1000 | 2413.177649 | 7.03550335 | 180526217.3 | 0.043146801 | Small Building |
| 1421.36241 | 3430 | 10 | 364711900 | 0.087168236 | Small Building |
| 1719.019445 | 4148.299302 | 12.09416706 | 533460000 | 0.1275 | Small Building+ |
| 2407.108692 | 5808.780895 | 16.93522127 | 1046000000 | 0.25 | Building |
| 3553.406026 | 8575 | 25 | 2279449375 | 0.544801476 | Building |
| 4632.2266 | 11178.3857 | 32.59004576 | 3873645510 | 0.925823497 | Building |
| 5000 | 12065.88825 | 35.17751675 | 4513155433 | 1.078670037 | Building |
| 5106.248638 | 12322.28508 | 35.9250294 | 4707000000 | 1.125 | Building+ |
| 6808.331517 | 16429.71344 | 47.9000392 | 8368000000 | 2 | Large Building |
| 7106.812052 | 17150 | 50 | 9117797500 | 2.179205903 | Large Building |
| 10000 | 24131.77649 | 70.3550335 | 18052621734 | 4.314680147 | Large Building |
| 12273.89419 | 29619.08713 | 86.35302371 | 27196000000 | 6.5 | Large Building+ |
| 14213.6241 | 34300 | 100 | 36471190000 | 8.716823614 | Large Building+ |
| 15966.95272 | 38531.09343 | 112.3355494 | 46024000000 | 11 | City Block |
| 35865.11175 | 86548.88606 | 252.3291139 | 2.32212E+11 | 55.5 | City Block+ |
| 48142.17384 | 116175.6179 | 338.7044254 | 4.184E+11 | 100 | Multi City Block |
| 50000 | 120658.8825 | 351.7751675 | 4.51316E+11 | 107.8670037 | Multi City Block |
| 100000 | 241317.7649 | 703.550335 | 1.80526E+12 | 431.4680147 | Multi City Block |
| 112903.4055 | 272455.9745 | 794.3322873 | 2.3012E+12 | 550 | Multi City Block+ |
| 142136.241 | 343000 | 1000 | 3.64712E+12 | 871.6823614 | Multi City Block+ |
| 152238.9209 | 367379.5611 | 1071.077438 | 4.184E+12 | 1000 | Small Town |
| 280714.6998 | 677414.4393 | 1974.969211 | 1.42256E+13 | 3400 | Small Town+ |
| 366639.8728 | 884767.1463 | 2579.496053 | 2.42672E+13 | 5800 | Town |
| 500000 | 1206588.825 | 3517.751675 | 4.51316E+13 | 10786.70037 | Town |
| 1000000 | 2413177.649 | 7035.50335 | 1.80526E+14 | 43146.80147 | Town |
| 1107269.998 | 2672039.212 | 7790.201783 | 2.21334E+14 | 52900 | Town+ |
| 1243174.12 | 3000000 | 8746.355685 | 2.79E+14 | 66682.60038 | Town+ |
| 1522389.209 | 3673795.611 | 10710.77438 | 4.184E+14 | 100000 | Large Town |
| 3570319.168 | 8615814.417 | 25118.99247 | 2.3012E+15 | 550000 | Large Town+ |
| 4814217.384 | 11617561.79 | 33870.44254 | 4.184E+15 | 1000000 | Small City |
| 5000000 | 12065888.25 | 35177.51675 | 4.51316E+15 | 1078670.037 | Small City |
| 6371000 | 15374354.8 | 44823.19184 | 7.32749E+15 | 1751313.182 | Small City |
The table below lists out the energy required to send a person flying at a speed across a distance using the relativistic energy model.
| Range (m) | Speed (m/s) | Speed (Mach) | Energy (Joules) | Energy (ton TNT) | Tier |
|---|---|---|---|---|---|
| 1243174.12 | 3000000 | 8746.355685 | 2.79021E+14 | 66687.60755 | Town+ |
| 1522389.209 | 3673795.611 | 10710.77438 | 4.18447E+14 | 100011.2643 | Large Town |
| 3570319.168 | 8615814.417 | 25118.99247 | 2.30263E+15 | 550340.9371 | Large Town+ |
| 4814217.384 | 11617561.79 | 33870.44254 | 4.18872E+15 | 1001127.7 | Small City |
| 5000000 | 12065888.25 | 35177.51675 | 4.51865E+15 | 1079982.279 | Small City |
| 6371000 | 15374354.8 | 44823.19184 | 7.34198E+15 | 1754775.208 | Small City |
One thing: I include a data set for a distance of 4632.2266 m as the farthest horizon a human eye can see. Working:
Average US human height = (1.753 + 1.615)/2 = 1.684 m
Earth mean radius = 6371000 m
For two identical human to see each other at a distance, the farthest distance the one would travel away from the other standing still yet seeing each other can see each other = Arc(G1-M-G2) = 2 times Arc(G1-M)
G1-M = OM * angle(G1-O-M)
cos(angle(G1-O-M))= OM / (H1-G1 + G1-O) = 6371000 / (6371000 + 1.684)
angle(G1-O-M) = 0.00072708 rad
Arc(G1-M) = 4632.2266 m
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Findings - On Request (Re Battle for Dream Island)[]
Priority: 1 (Would scale to the whole verse.)
Verse: Battle for Dream Island
Assume a wooden stick at 60 inches weighs 610 g or 0.61 kg, a wooden stick at 8 inches should weigh 81.33333333 g or 0.08133333333 kg.
Taking the distance literally, the stick must have thrown at over 2,760 miles which means possibly 4441789.44 m.
Since it stops at about 1 second, the stick must have flown at at least 4441789.44 m/s. 1.4805965% light speed man.
Assume Newtonian KE model still stands, KE yield = 8.02333E+11 J = 191.7621254 tons TNT (Multi City Block)
Assume relativistic KE model applies, KE yield = 8.02465E+11 J = 191.7937022 tons TNT (Multi City Block)
Findings - Credits to Psychomaster35 (Re Battle for Dream Island)[]
By comparing the stick to Pin's height (see this for reference), the stick should be 27.92699307283465 inches and 0.283924429574 kg.
Taking the distance literally, the stick must have thrown at over 2,760 miles which means possibly 4441789.44 m.
Since it stops at about 1 second, the stick must have flown at at least 4441789.44 m/s. 1.4805965% light speed man.
Assume Newtonian KE model still stands, KE yield = 2.80084E+12 J = 669.4174436 tons TNT (Multi City Block+)
Assume relativistic KE model applies, KE yield = 2.8013E+12 J = 669.5276767 tons TNT (Multi City Block+)