# B In jousting, how does speed affect the knight's lance?

1. Jun 18, 2017

### pizzae

Hi,

I don't have any background in physics at all (perhaps besides knowing about the relationship between speed, distance and time). Rather I am considering making some video game about jousting, and I'm considering whether a physics based approach would be good for the user experience.

Anyway, the context is that two knights are jousting. They both have armour and lances and shields. The main objective is to knock off your opponent from their horse. So you'll need enough power to do so. Gaining speed and driving your lance in them is what will knock them off their horse. Throwing a small pebble at their head won't do anything.

I got a little bit of help with this before, and I was told that these variables would come in handy for this situation: Power = velocity (distance/time) * force (mass*acceleration). I'm not entirely sure the difference between velocity and acceleration. And how weight would play part in this.

Without experience in physics, I am assuming that the faster a car crashes into a wall, the more damage it will sustain. A car moving slowly towards a wall at maybe 1km/h would only take minor scratches on the front, whereas a car speeding towards a wall at 100km/h would definitely crash and take more damage.

In that assumption, I am assuming that Knights who travel faster, will also take more "damage" or an impact (using that car example)?

And I'm also assuming that the faster one goes, the harder hitting they'll be. Getting hit by a car going 5km/h isn't as bad as getting run over by one going 100km/h. So I am assuming, in regards to "gameplay", that:
more speed = more damage dealt and more damage taken. Is that correct?

Given the following scenarios, what would happen to who? And who is more likely to take more damage/fall off their horse (relatively, and maybe with some proportions, e.g: Knight A takes about 30% more XXX)?
(We can assume that the speed they are travelling is 48km/h, if needed)

1. Knight A and Knight B are charging at each other, with the same speed and same equipment
2. Knight A and B have the same equipment, however, Knight A is more faster than Knight B (who takes more damage here and who is likely to fall off their horse?)
3. Knight A and B have the same equipment, but, Knight B is stationary, while A is charging really fast.

1A. Same as 1, but Knight A has heavier armour
2A. " "
3A. " "

1B. Same as 1, but Knight A has the same weight, but their armour is simply "better" (it can absorb better?)
2B. " "
3B. " "

Also, we can assume that the Knights might take damage too (from their HP) and I would assume it would be proportionate to the "impact" that they have taken.

2. Jun 19, 2017

### Staff: Mentor

Velocity is essentially your distance traveled divided by the time it took to travel that distance. A bullet traveling at 2500ft/s moves 2500 feet every second. A car traveling 60 mph moves 60 miles every hour.

Acceleration is the rate at which velocity changes. An acceleration of 10 ft/s2 means that every second your velocity changes by 10 ft/s. So if you start at 0 ft/s, after 5 seconds your velocity is 50 ft/s.

All of the following is a "realistic" scenario that may not apply in exactly this way to a video game.

All of these situations essentially identical. This is because velocity is relative. By that I mean that knight A can think of himself as standing still and it is knight B who is charging (at double speed) at him. The reverse is also true. Knight B can think he is standing motionless and it is knight A charging at double speed towards him. From the standpoint of the actual collision, it makes no difference. Similarly, a car crash where two cars hit each other going 60 MPH each is identical as a crash where one car is stationary and is hit by another car going 120 MPH. The closing velocity (sum of the two speeds) is what matters, not each individual speed.

What matters here is things like where does each knight's lance hit? Does one hit and one miss? Do they both hit, but knight A is able to get in a high blow that flips knight B backwards off of his horse, while knight B gets a low blow that knight A is able to absorb by keeping a hold of his horse and saddle? Perhaps knight A hits knight B, but the lance deflects off of the slope of the armor, doing little.

I'm not a jouster, but I would think that heavier armor is generally advantageous. It increases the knight's mass and thus their inertia, meaning that it takes a larger force to accelerate them. If knight A has twice the mass of knight B, it's going to be very difficult for knight B to knock A off of his horse. Of course, all that extra weight makes it harder to move around and wield your lance, so there's a bit of a price elsewhere. And if your armor is too heavy, your horse puts in his two-week notice and quits.

The equation for acceleration is $a=\frac{f}{m}$, where $f$ is force and $m$ is mass. If you double the mass while leaving the force the same, the acceleration is cut in half. So you'd need double the force to get the acceleration back up to where it was. In layman terms, this means that a knight is harder to knock off his horse by a factor roughly equal to the increase in mass. AKA, if knight A is 30% heavier than knight B, A is going to be about 30% harder to knock off. This is a rough estimate only as we're only dealing with acceleration here. Other factors may make a good bit of difference, though since this is for a video game we can modify things however we please.

This isn't specific enough to really say much about. What does "better" mean? What does "absorb better" mean? Usually we mean that something can take a larger force without deforming or breaking. This is certainly important if your knights have armor which is breaking all the time, but otherwise it's not very important as far as I can tell. At least not in this simplified scenario we're working in. That doesn't mean that you can't make it into a gameplay factor though. Perhaps your player's knight can use money from his victories to upgrade his armor in some way and take on more challenging opponents.

If I remember the movie "A Knight's Tale" correctly, jousting is a point-based game. Hitting your opponent is worth points based on where you hit them and unseating them is either a win or worth a lot of points. Your version can certainly use different rules though. I mean, why not? Who says it has to be the same exact game as back in Medieval days? Perhaps instead of HP you can use "stamina" or "fatigue"? It's all up to you.

3. Jun 19, 2017

### pizzae

Sorry I still don't understand the difference between acceleration. If power = speed * force, and force has "acceleration" in it, doesn't that mean power = speed * mass * speed (again)? So the power of a small rock (given mass of 2) thrown at 5 units per second could be = 5 * 2 * 5?

For simplicity sake, we can assume that the knights just hit each other on the torso. Being hit in the head, or a non-direct hit (i.e, not hitting at a perpendicular angle) are not considered.

I was told that given two equal cars A and B are going to crash with each other, if B suddenly stops before the collision, that when they collide, B will go flying backwards (more so than A)? Wouldn't that mean that B would take more of an impact?

We can assume that given a heavier knight, they'll still be able to travel with optimal speeds, as the same as another knight who is lighter. The horse getting tired and having to exert more effort can be calculated outside of this.

How do we also differentiate between the force dealt and force taken? Or rather, the force that put out, and the force "resistance"? For example, A vs B:

A) A knight with full body armour, with a weak bamboo lance (easily breaks)
B) A knight with little body armour, with a strong steel lance (doesn't break)

Force does equal mass * acceleration, but how would I use that in the context of a game? More specifically, how does an opponent having more mass protect themselves better against my lance?

I tried writing out some example "equations":
-force1 = 2kg x 48 km/s = 96
-force2 = 3kg x 48 km/s = 144

But I'm not entirely sure how I would use such numbers. We can assume that these are the force coming from a lance of two different masses. The bigger mass will be more harder hitting of course. The question is, how would these forces be offset, or reduced by the opponent's armour? E.g: Total force dealt = 96 - ???

And can weight be used for mass? Or is mass something arbitrary? (Perhaps its the total number of atoms or something like that) And I'm assuming that there could be objects in real life with the same mass, but have different sizes/weight? e.g: A small pebble and an ounce of gold, the gold is heavier, but would they both have the same mass, or would the gold have more mass too?

Also, regarding weight and mass, which of the following would be more "harder hitting" and heavier?
1) A twig
2) A wooden lance
3) A pure gold lance

Last edited: Jun 19, 2017
4. Jun 19, 2017

### Staff: Mentor

No, the rock isn't exerting a force over the distance that it travels (ignoring the small force on the air that it shoves out of the way).
The units of power don't really matter here. They're confusing if you've never done physics before and I can't imagine where we'd need to account for that.

B will go flying backwards more than it would if it were moving forward, but the severity of the crash would be identical for both vehicles. The reason being that Newton's laws tell us that the force exerted on an object A by object B is equal and opposite to the force exerted on B by A. If both vehicles are subject to the same force, then the severity of the collision is the same for both vehicles (assuming they are the same type of vehicle of course).

The reason the car would go backwards more so in this scenario is that it isn't moving and so the force exerted during the collision accelerates it backwards instead of slowing it down.

The force exerted by a lance on a knight is equal to the force exerted by the knight on the lance. Your choice of lance material would influence how easily the lance breaks and a few other things, but these aren't very easily calculated with any real accuracy.

Unfortunately I can't answer how you'll use these in a game. You could opt for a more realistic game, but this can be much harder to develop, especially if you haven't taken a physics class or two. It's difficult to explain how things like acceleration and force play into all of this if you have no working knowledge of these concepts.

No, you'd need to use mass. Kilograms are already a unit of mass, so you can use those, but pounds are not. Instead you'd need to use the slug. Or just skip all that and use pounds for anything involving force since pounds are a unit of force (weight is a force).

Unfortunately it's not quite this simple. In real life a gold lance would be impossible to wield and would probably bend so much under its own weight that it would be completely unusable. A wooden lance is a good mix of strength, weight, and flexibility.

5. Jun 19, 2017

### jbriggs444

Weight (the force required to hold something up against gravity) and mass (how hard it is to accelerate something) are proportional. Double one and you've doubled the other.

In the U.S., the "pound" is an ambiguous term. It can be used to refer to mass (a five pound bag of sugar) or force (a spool of 20 pound test fishing line). The mass of a U.S. pound is standardized at 0.45359237 kg exactly. The pound force is the weight of a pound mass.