# How magically increasing external muscle strength will influence common activities like running?

My Mary Sue Marty Stu has a divine blessing which increases his muscle strength threefold. This has relatively precise meaning: if before blessing he could push horizontally some weight with the force of, say, 500N, after the blessing he pushes with the force of 1500N. Muscles at the moment of pushing started contracting and the resulting motion of limbs should have been exerting 500N of force but the blessing added 1000N more.

To preserve 2nd law of thermodynamics the energy to increase the force comes, say, from some distant star. It's the deity we are talking about.

Given such a blessing, how the routine activities change for my character?

1. Running (how the speed and the motions themselves change)
2. Jumping (how the height/length and the motion itself change)
3. Grappling, climbing
4. Punching, kicking things
5. Pulling, pushing things
6. ???

Are there any caveats I should be aware of? I came up with two caveats:

1. There are muscles inside the body, especially the heart. This is solved by blessing only external muscles, the ones directly below the skin which move our limbs and keep the spine and belly.
2. Neural system is not accustomed to increased effect of the motions. The accommodation process is the important part of the plot.

Thank you. :)

EDIT 1 I must note that the basic idea behind the blessing is that the strain on the muscles does not increase. Energy expenditure of the body stays the same - only the resultant effect is tripled. If it's implausible I would love to read the deconstruction - it will help me modify the idea!

EDIT 2 I understand that to keep normal behaviour the character in question will need to accommodate to do the same motions with less force than he was accustomed to. My question is about the effects of tripling the strength. If there's backlash to it, so be it. :)

• If the energy is transfered from a distant star, the first thing that happens is that all actions are delayed by the time light needs to travel from that star. What you are describing is accomplished by some actual humans without the help of deities that we know of (but maybe with some drugs) – Raditz_35 May 8 '17 at 13:01
• I do hope you've increased bone strength to match – Separatrix May 8 '17 at 13:07
• @Separatrix and all related connective tissue as well – Richard U May 8 '17 at 13:31
• This is an interesting quesiton, but incredibly broad. The effects of this on every aspect of life would be enrmous. I think you're going to need to narrow this down to just one aspect (or maybe two related aspects). The caveats should probably be a separate question. – DonyorM May 8 '17 at 21:33
• @hijarian aaahahahaha :-D Oh, god, I hope you didn't misunderstood. I was not complaining about anything, go figure, just trying to improve my English. Maybe the term "Mary Sue" in English is neutral, I can't know if I don't ask :-) – motoDrizzt May 9 '17 at 6:56

# Regarding bone and tendons

First, let us assume that the physical parts of the body can handle the additional strength. A 175 lb trim person can bulk up to 250 lb and triple their strength in most weight-lifing measures; 50 lb + weight gains are par for the course for professional NBA or NFL players. This is accomplished while not breaking any bones or tearing any tendons (usually, though such injuries are relatively more common in pro athletes). However, this person's agility and movement is now limited by their new weight.

The chief advantage of this magical strength blessing is the increase in power to weight ratio. If you could maintain your 175 lb mass but triple your strength, you would see significant benefits in speed and agility. Now to use a sports analogy, just because you are 175 lb but as strong as a 250 lb defensive end doesn't mean you can do what a defensive end does. Your mass is still low, and mass counts for a lot in certain kinds of combat (such as blocking NFL linemen, or tackling). However, if you are 175 lb and as strong as a 250 lb NBA power forward, or NFL running back, you will see the large returns on your agility.

So regarding combat overall, it depends on what you are doing. Getting stronger won't help you as much in combat that depends on the push (locking shields Greek phalanx style, or charging an opponent with a couched lance) but will help you a lot when you can combine strength with agility (shooting a composite bow from horseback, throwing javelins, or dueling with swords)

# Specific motions

Running is limited by the force of gravity pulling you down. You take a stride and then you have to be pulled to the ground by gravity in order to make contact with your next stride. Increasing your stride rate is an option, but not as good of one: increased rate causes increased friction and will cause cooling problems. Someone with a magical strength blessing would be better off looking somewhat like the astronauts on the moon, hopping around with unbelievable stride lengths. However, this would take some time to get used to, and you might not really be able to utilize your full power.

Jumping is much more straightforward. The work done by a jump is force times distance; if your legs are just as long and the force increases by a factor of 3, then the distance increases by a factor of three.

The work done by the jump will all be converted to potential energy at the height of the jump. So $F\cdot d = m g h$. Since distance, mass, and gravity are all constant in this case, force is proportional to the height jumped. If you can jump with three times more force out of your muscles, you can jump three times higher. An impressive initial box jump of 1 m would turn into an unbelievable box jump of 3 m.

Unfortunately, as @JasonK points out in the comments, landing from a 3m fall isn't exactly trivial. Humans just don't jump that high. You may have enhanced strength, but you don't have enhanced durability. Even if you have good technique, jumping this high frequently will get you a sprained ankle or stress fracture sooner or later.

Grappling is something where you will be limited by mass. Instead of the ratio of your power to your weight, what matters is the ratio of your power to your opponents weight (and his power to your weight). For example, if the 175lb trim blessed warrior is 20% stronger than his 250 lb opponent, he is still at a disadvantage due to the mass disparity being more than 20%, assuming fighting skill is equal. This would be the classic MMA battle of striker vs. wrestler, where your blessed character would work hard to avoid the ground and pound. Climbing wou

Climbing, punching, kicking, pulling, and pushing should all scale about linearly with increased strength, at least for reasonably small strength gains like a factor of 3.

• Holy cow, from 0.8m jump to 7.3m jump!!! I couldn't even imagine such powerful effect, and thank you for the formulas. Also, is there any formula relating total running speed with the individual stride length / force? – hijarian May 8 '17 at 14:46
• @hijarian Not really. Running speed is highly mechanically dependent. Animals that run really fast (like cheetahs) have a lot of specific adaptations related to flexibility, oxygen intake, and body cooling. Strength, I think, is a relatively minor part of running fast. I don't think your hero would get as much running advantage from strength as jumping. There is a reason they always show Hulk jumping everywhere. – kingledion May 8 '17 at 15:05
• The real risk is LANDING. He is magically protected from muscle shear while JUMPING, but he will fall the same, so he has a very real risk of jumping too high and crashing back to earth at speed, breaking bones. On the moon the downward acceleration is proportionately less so it sort of compensates for the jumping lope astronauts use, but this wouldn't be the case on Earth. – Jason K May 8 '17 at 15:13
• @JasonK Very good point about landing, I edited it into the answer. Regarding sprinting, Usain Bolt is 6'5", 207 lb; Dennis Kimetto, the marathon world record holder is 5'7", 121 lbs. They are mechanically very different. Also, since a lot of high schoolers can do an 11 sec 100m; Bolt is in reality probably only 10% faster than Kimetto, despite his muscular advantages. If the hero is 10% faster than Bolt, that is amazing at the Olympics, but doesn't exactly make you the Flash. – kingledion May 8 '17 at 15:19
• @humn Yep I messed that up. I reformulated in terms of work vs. potential energy to make it simpler. Should have thought of that in the first place. – kingledion May 8 '17 at 18:09

You're only considering strength, but our superhero pals have other issues, most notably of an energetic and thermodynamic nature...

• Base strength

If the superhero is a wet noodly nerd, and we multiply his strength by 3, he probably won't get as strong as a normal bodybuilder... So he's still gonna need to go to the gym! However he'll get 3x more benefits than a normal guy.

• Techniques

A scrawny black belt has a good chance of wiping the floor with a meathead who doesn't know how to fight. So your guy will have to sign up on a dojo or something.

• Self-preservation

We have sensors in our tendons to make sure we don't rip them out. They provide feedback to the muscle. People who experience convulsions or uncontrolled muscle contractions can pop joints and snap ligaments... So gotta suppose his bones, tendons and joints have been upgraded too. He's also gonna need special shoes and gloves... 'cause you can destroy your knuckles when punching something with normal strength, so super-hero strength is even worse! After breaking his wrists a few times, I'd guess he's gonna opt for a sword or something.

PS: head-butts wouldn't be a good idea.

• Speed

With 3x the strength he can swing a sword 3x as fast, or swing a heavier sword at normal speed and hit harder. There's a compromise here. Punching or running might be limited by other factors (ie how fast the muscles can contract) and of course if his brain/nerves runs at normal speed or not.

Being startled and jumping up might result in head-butting the ceiling.

• Energy

Our muscles use energy storage molecules (ATP and Phosphocreatine) which are immediately available but have very limited capacity (a few seconds of effort). These are replenished by mitochondria using respiration if there is enough oxygen present, or lactic fermentation if there is not.

So, your superhero might have super-strength, but the same energy reserves as a normal human... in which case he'll punch super hard, but tire a lot quicker. You'll also need to boost his recharging rate by star magic influx... but there might be various inconveniences before he gets used to it.

• Power and endurance

If he climbs uphill 3x faster than a normal human, then he'll use 3x the power, which means he'll need 4 extra lungs and 2 extra hearts to process the extra oxygen to produce this energy.

Okay, star magic.

• Heat

We're only 25% efficient, so when we expend 1 joule in muscle output, we heat up by 3 joules. If his power triples, his heat output will also rise... so he might cook himself to death.

The fairy could give him a more efficient metabolism.

• Just because you're 3 times stronger, doesn't mean you can wield a weapon 3 times faster. A 100bhp car can drive 150km/h, a 600bhp car 400km/h because drag increases exponentionally. Same goes for warming up. Yes, you warm up a lot more, but that heat dissapated faster as well :) You're answer isn't wrong, just a but inaccurate. – Martijn May 8 '17 at 14:54
• Yeah I didn't mention running speed because the relation with power is much harder to get than for, say a bicycle... Air drag force is in v^2 so drag power is in v^3 (not exponential btw) however most of the power needed to run isn't used against drag but simply to hop, so I have no idea how much faster he would go!... (upper bound 3x, lower bound 1.4x, but probably at the speed of plot) As for a sword, I was thinking the speed limit would be due to rotating the sword's mass (inertia) so more strength (force) would make it swing faster, same for throwing a big rock... – peufeu May 8 '17 at 15:38
• Also Mike Tyson was rumoured to punch 1600 joules which is HORRENDOUSLY HIGH, if our superhero does 3x that then anyone's head is a watermelon, but his knuckles are going to be single use. – peufeu May 8 '17 at 15:41
• I disagree with your second point. If you are 3x stronger, and already strong to start with, you will be moving much, much faster as well. You can touch the black belt and instantly kill them pretty much. – theonlygusti May 8 '17 at 16:18
• I was thinking about scrawny-shrimp nerd-guy gets blessed with super-strength, puts on a cape, hits the street, puffs his chest... and gets beaten up (bit like the movie Kick Ass actually!) – peufeu May 8 '17 at 17:17

I am afraid that increasing muscle strenght by a factor 3 and leaving the bones and tendons the same will work like installing a 500 cc engine on the chassis of a 50 cc scooter: the chassis will soon get broken by forces exceeding its operating range.

If you push 1500 N with your arm, your arm is also receiving a 1500 N push (good old Newton's law). If your bones and ligaments are not used to withstand that force, they can break, immediatly or over time.

• I would try to elaborate. If we imagine this blessing as the additional "hand" which holds the arm. And when the arm is pushing something with force of 500 N this helping hand pushes the arm more, adding another 1000 N. Then the arm which pushes receives the tripled feedback. Do I understand correctly? This is enormously helpful feed for thought. – hijarian May 8 '17 at 13:50
• No, if the blessing acts like another person/tool exerting force, than the reaction force perceived by the subject won't change. If instead the blessing simply increase the muscle strenght of the subject, the reaction force will change. – L.Dutch May 8 '17 at 13:58