Accounting for Relativistic KE in the Kinetic Energy Section of Large Size Calculations

[Flashlight237]

As it currently stands, the Large Size Calculations page only accounts for Newtonian KE. Generally, it is preferred that we use relativistic KE starting at 1% the speed of light. The site's cap at which relativistic KE can be allowed at is at 4x Newtonian KE, which is achieved at exactly 278988318.1 m/s (~93.06% the speed of light).

As such, I first decided to see where the cap for Newtonian KE would be located for both male and female humans. It would be as follows:

Male: 2997924.58/5.55*1.71=923684.8706 meters
Female: 2997924.58/5.55*1.595=861565.7126 meters

This in essence makes the maximum mass as follows, note that the 62 kg value used for mass is apparently unisex in the Large Size Calculations article itself:

923684.8706³/1.71³*62=9.771806283*10^18 kg

For a maximum newtonian KE as follows:

9.771806283*10^18*2997924.58²/2=4.391230751*10^31 joules

This, in essence, means that the highest rating allowable with Newtonian KE on the menu is Low 5-B.

As for the maximum relativistic KE allowable (a speed of 278988318.1 m/s), here's what I got.:

Male: 278988318.1/5.55*1.71=85958562.89 meters
Female: 278988318.1/5.55*1.595=80177723.85 meters

The most readable method of which I can show off certain energy requirements accounting for relativistic KE is through a Desmos graph.: https://www.desmos.com/calculator/o8jagthair

I have noted the following size requirements for men:

Low 5-B+ (1.25254316*10^32 joules): 1139082.58122 meters; 3679022.413 m/s
5-B (2.4869696*10^32 joules): 1306554.82574 meters; 4240572.68 m/s
5-B+ (8.07394848*10^33 joules): 2620422.53086 meters; 8504880.144 m/s
5-A (1.58992*10^34 joules): 3000632.8026 meters; 9738895.938 m/s
5-A+ (3.45510536*10^37 joules): 13906144.78 meters; 45133978.69 m/s
High 5-A (6.9086208*10^37 joules): 15955629.05 meters; 51785813.59 m/s
High 5-A+ (1.57350031*10^40 joules): 45544900.07 meters; 147821166.9 m/s
Low 4-C (3.265612*10^40 joules): 51574418.88 meters; 167390657.8 m/s
Low 4-C+ (3.00350532*10^41 joules): 73913837.04 meters; 239895786.9 m/s
4-C (5.69300144*10^41 joules): 79975710.85 meters; 259570289.6 m/s

You should be able to get the height figures for women if you multiply the height values for men by 1.595, then divide by 1.71. As such, you'll get the following:

Low 5-B+ (1.25254316*10^32 joules): 1062477.612 meters; 3679022.413 m/s
5-B (2.4869696*10^32 joules): 1218687.104 meters; 4240572.68 m/s
5-B+ (8.07394848*10^33 joules): 2444195.285 meters; 8504880.144 m/s
5-A (1.58992*10^34 joules): 2798835.86 meters; 9738895.938 m/s
5-A+ (3.45510536*10^37 joules): 12970936.21 meters; 45133978.69 m/s
High 5-A (6.9086208*10^37 joules): 14882589.67 meters; 51785813.59 m/s
High 5-A+ (1.57350031*10^40 joules): 42481938.95 meters; 147821166.9 m/s
Low 4-C (3.265612*10^40 joules): 48105963.81 meters; 167390657.8 m/s
Low 4-C+ (3.00350532*10^41 joules): 68943023.44 meters; 239895786.9 m/s
4-C (5.69300144*10^41 joules): 74597277.37 meters; 259570289.6 m/s

Through relativistic KE, I am able to add Tier 4-C onto the Large Size KE list, but no further. To make this all readable, I made a blog specifically for a copy-pastable table: https://vsbattles.fandom.com/wiki/User_blog:Flashlight237/Large_Size_Relativistic_KE_Table

It's mostly the same aside from accounting for revisions made to Tier 5-A, but around High 5-A+, you should see how relativistic KE makes things noticeably different. So yeah, there you have it.

 

[Kachon123]

I like this. Looks good, nice job.

 

[Flashlight237]

Bump

 

[Flashlight237]

Bump

 

[Flashlight237]

Might have to resort to this...

@KLOL506 @Dalesean027 @Drite77

 

[Drite77]

I'll be busy for the next hours, will try to check this when I can

 

[Flashlight237]

I'll be busy for the next hours, will try to check this when I can

Okie-dokie.

 

[KLOL506]

Out of my realm of expertise, will recommend @DontTalkDT and @Executor_N0 to take a look.

 

[DontTalkDT]

One small correction: We don't limit the speed to 278988318.1 m/s, we limit the relativistic gamma to 4.

The kinetic energy value calculated using the formula for relativistic kinetic energy is only accepted to the point where it is 4 times as high as the value of Newtonian kinetic energy. That is the case, if the speed of the moving object is above 93% of the speed of light. For kinetic energy values above that, which are not faster than light, 4 times the kinetic energy value should be taken.

(also I realize now that the last sentence there should have the word "newtonian" in it)

So, in principle, the maximum allowed KE is 4*(0.5*m*c^2).

 

[Flashlight237]

One small correction: We don't limit the speed to 278988318.1 m/s, we limit the relativistic gamma to 4.

(also I realize now that the last sentence there should have the word "newtonian" in it)

So, in principle, the maximum allowed KE is 4*(0.5*m*c^2).

I know that; the math I did to figure out where that point was and 278988318.1 m/s is that point where the relativistic gamma is 4. Here's the graph showing that: https://www.desmos.com/calculator/koxtkkgbjk

 

[Drite77]

I might be too busy with the Calc Eval Thread, so I don't know if I can comment here in due time, there is a lot of stuff pending evaluation over there, so it would probably be better if other CGMs were notified about this

 

[DontTalkDT]

I know that; the math I did to figure out where that point was and 278988318.1 m/s is that point where the relativistic gamma is 4. Here's the graph showing that: https://www.desmos.com/calculator/koxtkkgbjk

So when you say "maximum relativistic KE allowable" you mean "maximum size at which the regular relativistic KE formula can be used, without rounding down to relativistic gamma = 4" not "maximum value for KE a large size character can reach taking into account relativistic KE and our rules"?

 

[Flashlight237]

So when you say "maximum relativistic KE allowable" you mean "maximum size at which the regular relativistic KE formula can be used, without rounding down to relativistic gamma = 4" not "maximum value for KE a large size character can reach taking into account relativistic KE and our rules"?

Both; the second graph I linked specifically answers the former part whereas the OP accounts for both.