Thursday, March 25, 2010

Physics of Fighting

I'm doing some exercises right now both physical and in math. Just testing out my understanding of physics and comparing it to games and real world.

In wikipedia i found some useful benchmarks for performance. A professional boxer can deal 450 joules of damage at 9 m/s. That is roughly 11kg or 22lbs of mass behind that force. I wish I knew if it was a light or a heavy weight. An arm being 3kg or 6.6lbs can let me determine what amount of the mass is the arm and the body.

In GURPS basic set, I feel that work or joules is a better measure for physical performance. Take for instance the Basic Lift score, which is based how much weight a character can lift over his head from a resting position in a second. Given an average character uses 5'9" to 5'10" that is an arm moving at 1.88m/s. At 20lbs or 9kg plus for ST10 that's around 21J (including the weight of the arm).

Bows have a whole lot of physics problems that go with it. A warbow, composite or yew, with a draw weight of 180lbs or 81kg and a war arrow at about 40g would be able to hurl that arrow up to 20m/s at perfect efficiency. Probably 75-85 m/s because of inefficiency.

Sword Physics.
When you compare a thrust and a swing, the former travels the length of the arm and the displacement of the shoulder as body weight shifts to add power to the thrust. While the swing travels a ~100 degree arc which has a distance equal to the displacement of the shoulder + length arm + the blade multiplied * 2 * 3.14 * 100/360 at roughly the same amount of time. So you have the blade serving as a lever and significantly increase the force of the swing compared to a thrust.

I'm 5'9" (176cm) my arm is around 60cm from the sleeve of the shoulder to my knuckles. So If I thrust, drawing my fist to my shoulder elbows pointed back and turning my torso back, my fist travels the length of my arm, the distance my shoulder twists and my footwork covers.

Trying to calculate a light thrust with a 21J character. Since there is considerable effort, I will bump up the factor of effort equal to an action comparable to the Fatigue expenditure of combat. That would be half of walking (basic move * 1.11 at FP per hour B426) to Paced Running (move basic * 2.5 at 1FP per hour) which is x1.13. At 24 joules sword will 3.25 m/s. This means the in one second, a thrust traveling the length of the arm with the torso turning along with it, which is 1m or equal to 1yrd reach, would take 0.3 sec or 0.5 second as arm recoils to a guard position. This assumes no footwork.

Assume the arm was around ~6.6lbs (~3kg), and the sword weight ~1.5lbs (~0.7kg).
That is 36% the speed and performance of a professional boxer.

Now that I know how much time I can probably calculate the speed of a sword swing.
How much force will I be generating if I swing with a Fullham Gladius where the tip of the edge would be traveling 3.85m and the the broad chopping edge would be traveling 3.15m?

An attack of that occupies the same time, but with the leverage of the length of a blade would be traveling 10.5 m/s. With the same weapon and mass, the attack is around 248J.

So a ST10 character, by gurps physics thrusts at 24J while swings at 248J with a shortsword.

Physics for a game system.
Physics is pretty complicated as a basis for a game system. I hardly remember my gradeschool physics what more high school. I only get practice because of game design tools and exercises.

I don't hear much of it used for games. I know that Mount&Blade actually uses physics to determine damage, because the game designers were such geeks they wanted to know more about mounted combat within the limit of their budget. I know some pseudo physics are used for games, particularly in destruction sequences.

Other than GURPS, has anyone tried making a game system that can be modified to be more consistent with physics?

I remember the TV specials about martial arts masters and the forces they are able to employ. The values are pretty amazing, but they are not unpredictable. In fact, thorough athletics testing and science can pretty much scan for optimal performance method.

As for a table top RPG, with the great limitation and consistency the body can be predicted, why not just have a physics based fighting system that is open to be tinkered. I can think of a bunch of reasons why not: "if it ain't broke don't fix it", "its a fiction why bother", who "would want that kind of game system?"

I know I would. I mean, I pretty much learned history because of RPGs. I think I would have really jumped into my math and physics homework if I was solving for the following:
  • Calculate the amount of force needed to penetrate 2mm bronze plate among the bronze age weapons.
  • What would be the range of a Composite Bow at 25kg draw with 60g war arrows?
  • Create a ballista capable of damaging or capturing iron age galleys.
  • What is the fastest galley you can generate in the 6C BC if you had access to only X technology and Y materials.
  • Given X physical attributes, what technique can be used to disable Y kind of shields. The technique has to make certain requirements.
  • How much weight is the warrior shifting when he throws a punch in this Illustration? Calculate the probably force being exerted by the warrior with his blade.

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