Realistically calculating the movements of someone with super strength

Question

Let's start by assuming a superhuman that isn't limited by biology for obvious reasons. Then let's assume they also receive super toughness to make this work.
Their super toughness scales with strength, so that if they are 10x stronger than a human a normal blow will only harm them 1/10 as much as it would harm a normal person. This is more of a tentative rule, if this is inadequate to avoid really anticlimactic solutions then I will totally change it.
I'm also assuming other stuff like how many G's they can withstand before blacking out scale the same way.

Now the obvious thing I need to know, is if they have something analogous to muscles generating force within their body, how do you calculate how fast they can run and jump?
Obviously things don't just scale linearly, a man who can carry a few tons as much probably can't run supersonic, so clearly speed isn't linearly derived from strength.

For the purposes of this I will not be considering crazily high end superhero's, nor superhero's barely above human level. I am asking about the consequences of superhuman strength ranging from a lifting a ton, to carrying 10 tons. (metric or imperial your pick).

I am working on a setting that involves superhumans, and I want to be able to figure out what combat would actually look like, how fast they should actually be able to move and how high they could jump. By starting with their strength and working to figure out how other abilities are derived from that.
I am also assuming that where it matters the super's reflexes are sped up, and their perception of time is slowed down when they are moving fast, so that they can use the resulting pseudo-super speed effectively in combat.

The things I want an answer to cover are:

Given a particular amount of super strength, from a minimum of lifting a ton to being able to lift 10 tons at maximum, how high will they be able to jump and how fast can they run and otherwise move?

How would their movements apply to other movement situations, like moving inside buildings, for instance would you be able to run leaping from wall to wall.

Also more generally, how does super strength influence movement capabilities?
I can find dozens of sources talking about how super strong punches would work, but next to nothing covering basic extrapolations for movement.

For instance, how much of a limiting factor is the strength of surrounding materials to super strength enhanced movement, how much does it limit your ability to jump or run at full strength?
How plausible is it for someone with super strength to jump over buildings, or to get to the top of a skyscraper by wall jumping between it and another adjacent skyscraper?
How does the ability to rapidly accelerate and decelerate influence melee other than just being able to hit harder?

Suffice to say, I think mid tier super strength is probably way more versatile and just different than generally imagined.

To be extra clear the only power that matters here is the super strength, (though it also comes with super toughness and somewhat faster reflexes as required secondary powers.) Everything else should just be be about the logical extensions of super strength, specifically how it affects movement.

Bonus question: Given the massive force to mass ratio of these superhumans, they could certainly manage human powered flight through any number of means. Elaborate on a method you think would be particularly good.

Answer 1

Until you start dealing with air resistance, jumping ability should scale fairly well with strength. If you can exert a downwards force ten times as strong as an ordinary human, you should be able to jump ten times as high. This would damage the ground as much as if you were falling down from the same height. A person with super strength should be able to leap over a small building without trouble.

However jumping over a skyscraper will require significantly more force in order to overcome air resistance - a human can hit terminal velocity falling from a skyscraper. Since air resistance increases as you move faster, and our high-jumping hero cannot accelerate further after leaving the ground, higher jumps will result in diminishing returns for force outputted. If they can exert enough force to jump a skyscraper, they may very well tear up the ground they jump from; they may also set off a sonic boom if their initial velocity exceeds the speed of sound.

When running at super speed, the hero must take into account the fact that striking the ground hard with their feet will propel them upwards as well as forwards - when they are moving fast enough, they will probably be spending a lot of time in the air, moving in leaps and bounds rather than zooming along the ground like the Flash. Since they cannot accelerate further once they leave the ground, this will limit their top speed.

Jumping off walls or ascending between buildings should be comparatively simple - people do some impressive parkour in real life and are limited mainly by strength, agility, and reaction time, so a superhero should be able to do it significantly better long before hitting the points where physics becomes a problem. They will not be able to run up or along a single wall much more than an ordinary human though, as this is limited by the fact that hitting the wall harder pushes you away from it.

Answer 2

They definitely will need better shoes.

One 10t strength, with mass 100kg - will jump probably 100m high (or less because of air) with initial velocity ca 44 m/s, duration of jump 0.045sec, 4.5 sec fly up and 4.5 sec fly down times.

Height of jump is linear with force/strength, speed linear to sqrt(), so 5t man jumps 50m high, 31m/s velocity (44/sqrt(2)), 1t man 10m high, velocity ca 14m/s.
The calculation is a bit odd, I assumed they able to apply that force evenly along 1m acceleration path, and they limb working fast enough for that.

The nice thing, they can not worry about the strength of skyscrapers roofs, because they can fly Daedalus/Icarus style - less energy, more speed, safer, less skyscraper depended, more flexibility(no needs to sit on the tallest skyscraper and wait for action). Nowadays they may use kevlar instead feathers and wax, for they flying suits. Also how base jumpers shows(with their squirrel suits) it will be pretty fast, may be faster then skyscraper-jumping, and definitely more flexible in therms of trajectory.

That initial sped, 44m/s, for 10t man, is actually base speed for all his legs, arms movements. If assume 10kg each, 10t divide by 2(2 arms have 10t combined), apply sqrt(5) - it's ca 100m/s limit.
Not bad actually, definitely he can crash walls, etc like 20-pound ancient cannon, or trow something pretty massive(for that speed) with similar results.

Run speed is limited by the speed of leg movements - so 100m/s best max for 10t man, so no sonic booms whatsoever. Probably he will move faster by flying with some suit extensions. Using all his 4.5 limbs. His total power is 6000 horse power (10t force per 0.045sec for 2 limbs is 3000 horse power) - for aircraft with much less power and higher drag - makes 600km/h La-5. So theoretically speaking it's enough for 2Mach speeds. So subsonic speeds he will do, and it's 3 times faster than the maximum speed he can run with same assumptions. So I would suggest buy kevlar wings, and sell it to that 10t man, with 300% profits.

If he can't do that 6000 hp constantly for a long time - then yes jumping may be a good option, but still not much better then gliding, and wings will help to manage that jump trajectory like squirrels do.

Fight
One punch, with 10kg arm and 5t force, will have duration 0.02sec, so if you haven't ended your opponent in 1 second with 100 punches, probably your actions are useless and you should go and take .50 BMG - will solve your problem, if not, you sucks, he rocks.

Equilibrium(film) is actually nice representation of that style fights. Not exactly, but looks like they keep that in mind.

Force and buildings 10t is a lot if applied on a small surface. Ability to withstand 20t force per square meter that is pretty strong and usually overkill, from an industrial point of view, for common situations.
So roof workers will definitely ask, who should pay for that damage. Everything may be tested with old canon blasts, if it will stand then it will stand the man.

Actions in compartments
As typical duration, at max speed(100m/s) movements, are 0.02 and that is 7-10 times lesser than typical human reactions so to use and be able to manage movements during that time, 10tman should react at least 10 times faster then average human. To be able tune his movements during the movement itself, I would say, he should be 30 times faster then average human, at least. (100 times and he will be fine, and do miracles)
Less volume room is, less percentage of his ability's 10tman can use. But definitely he can run walls, ceiling(not suspended ceiling obliviously, real one). You can imagine that by imagine average human in less gravity(0.001g) in room where surfaces are covered with ice, but faster you move more centrifugal force it is, less icy it is(and more muddy it becomes), then icy walls breaks. And that all takes 0.1sec instead minutes with average human in icy room.

Needs to add: Probably big volumes are also bad for such action. More you in the fly, more time you have troubles to control your actions-trajectory, and probably wingsuit is a must have item, but jumping of solid surfaces(those which withstand 20-pound cannon blasts, vaults and such) will be more efficient. The action is a combination of both - and actually very complex one. Not all distances between opponents are equally good, depends on the weapon.

Let say some one jumps with speed 44 m/s, at duration 0.02sec it is a travel distance about 1m. Uzi shoots 350m/s bullets, so in a room with distances 20m, as an example, it will take for a bullet 0.06 seconds to cover the distance. And it's not the fastest or most powerful weapon. 0.06 seconds time means - if you can't control your trajectory for about 3 meters - you may be vulnerable to such type of attack(if you against a similar villain, which can react fast enough). If they are vulnerable to the kinetic weapon (and that may be actually not the case - depends on where their strength comes from) then having two one shot gunknifes is a good idea. And all tactics is around how to place good single shoot. Automatic will not work on 100g actions, but it can be used if that's taken in to account, but 1 shot will work at any time.

Actually, close combat isn't a bad idea, because it will downplay many possible weapons and upplay individual characteristics like reaction time, and that is not so much different than usual close combat strategy.

Reaction time
All that wonders 10tman needs only against another 10tmans only. 9t man is no competition for him, 11t man is over powered for him.
The difference in speed of reactions between highly trained man and the average person is actually small. You may google for Isao Machii, he performs some showcases, didn't found original video for pellet cut, they have measured his typical reactions, he was some percents faster than average, but not so much (10% better, something like that, though not sure about the exact number).

So reaction time makes a huge difference in the results, with small changes to it one get a lot of advantages, with the same force. And be able to use full strength in motion is directly connected with speeds of reaction. So 100tman with human reactions is just big stupid rock, definitely, you do not wish to be caught by him, but if you do not do stupid things he is harmless.
Against any human few percents of 10tman ability's is overkill, except snipers, with average snipers involved just move more chaotic and 3 times faster than average human (but not forget snipers are not you enemy, stinger rockets are).

Technology is my god
The problem is a source of 10tman power. How it's done.

I can imagine such 10tman with technology's we already know, but which are not mature enough to do it right now. However, with those technologies, there is no place for fist fights, stuff trowing, skyscraper-jumping. Hulk will be destroyed in time way less than eye blink, like most of them who can't operate time, or be matterless(intangible).

That is just like a note, the source of strength is also important for strategy and tactics of such combat.