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The physics behind steelpushing


DoomslugTD

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Alright this is going to be a long one, but I got a few questions. First one is what equation do you think best describes the generall physics of steel pushing, or is there a better one I havn't thought of. This thinks of all objects as point masses. 

F is force 

O is allomatnic output (This puts together all the purity of metal/ strength of allomancer stuff)

M is mass of allomancer

m is mass of metal 

R is range 

d is distance between allomancer and object. 

f() is some undertimined function of the variables inside.

1. F = OMm {d<=R}

2. F = Om {d<=R}

3. F = O(M+m) {d<=R}

4. F = O*f(M, m) {d<=R}

5. F = O*f(m) {d<=R}

6. F = OMm(R-d) {d<=R}

7. F = Om(R-d) {d<=R}

8. F = O(m+M)(R-d) {d<=R}

9. F = O*f(M, m)*(R-d) {d<=R}

10. F = O*f(m)*(R-d) {d<=R}

11. F = OMm/d^2 {d<=R}

12. F = Om/d^2 {d<=R}

13. F = O(m+M)/d^2 {d<=R}

14. F = O*f(M, m)/d^2 {d<=R}

15. F = O*f(m)/d^2 {d<=R}

For the ones bellow range is determined using O and R is considered an arbitrary scaling constant if used. 

 

16. F = OMm {d<=RO}

17. F = Om {d<=RO}

18. F = O(M+m) {d<=RO}

19. F = O*f(M, m) {d<=RO}

20. F = O*f(m) {d<=RO}

21. F = Mm(O-d) {R<= 1, d<=RO}

22. F = m(O-d) {R<= 1, d<=RO}

23. F = (m+M)(O-d) {R<= 1, d<=RO}

24. F = f(M, m)*(O-d) {R<= 1, d<=RO}

25. F = f(m)*(O-d) {R<= 1, d<=RO}

26. F = OMm/d^2 {d<=RO}

27. F = Om/d^2 {d<=RO}

28. F = O(m+M)/d^2 {d<=RO}

29. F = O*f(M, m)/d^2 {d<=RO}

30. F = O*f(m)/d^2 {d<=RO}

The second question is somewhat encompassed within the previous one, but does the weight of the allomancer affect push strength. I have seen confliclicting results, both seeming to have merit but im wondering if there is WOB. In my head the book best lines up with the idea that it is dependent on weight because if it wasnt we would see kelsier (who weighed twice as much as vin) accelerate twice as slowly in any given scenerio as vin, irregarding any difference in allomantic strength, which is arguably not what happens throughout the books. Additionally when wax does his strongest pushes he always weighs way more, for example when he crushes the building he makes himself way probably somewhere close to several tons. People try to argue that it just let him stay in place which let him keep the same distance from the building causing the strong push but if he really weighed that much I doubt any steel push would have actually overcome the pull of gravity on him and he would have just fell albeit at a slower rate, and would have definitly not caused the amount of damage it did. 

My final question is about how many things you can push on at once. If you push on two objects do you push with half the force on each, or full force on both. If its full force is there a limit to how many things you can push on? if there isnt couldn't you just put a bunch of coins underneath you and push on all of them causing a massive amount of force as you do hundredes of simultanious pushes.

There is also another possibility for the functions that the mass of the metal you push on only effects the range of the steelpush and not the power, as from the book we can be pretty confident its not a 1:1 ratio for mass to power. 

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I do not remember any indication that the mass of the object or the allomancer affects push strenght, only allomancy strenght and distance.

Hence I would say F=O*f(d)

I further believe f(d) must be some kind of exponential decay, not a quadratic one like gravitation or electromagnetism, because allomantic strenght remains approximately constant at close range (up to 10-20 meters) and it becomes basically zero relatively fast after that.

Still, I'm not writing d<R because there does not seem to be a specific upper range, you can see larger metal objects at greater ranges.

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7 hours ago, king of nowhere said:

I do not remember any indication that the mass of the object or the allomancer affects push strenght, only allomancy strenght and distance.

Hence I would say F=O*f(d)

I further believe f(d) must be some kind of exponential decay, not a quadratic one like gravitation or electromagnetism, because allomantic strenght remains approximately constant at close range (up to 10-20 meters) and it becomes basically zero relatively fast after that.

Still, I'm not writing d<R because there does not seem to be a specific upper range, you can see larger metal objects at greater ranges.

I like this, It does seem that m might effect only the range, though I still like to argue that M as a place in the equation as well. Maybe it is of the form F=OM*e^-d {d<=Rm} or F=OM*e^-(d/m). 

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