Function Part Discussion

So, I was thinking, instead of making the wheel have multiple different detailed variations, it would be better to leave certain variables unknown, and then make that variable dependent on a specific property of the compound used, like we did for tools.

Now, here is just a general flow of my thoughts on handling wheels and motion for what you design in the Tech Editor. Beware of a long post.

Now, all Wheels should be the same FP, instead of having variants. What can change, however, is the material (compound) that the wheel is made of. This affects the properties of the wheel. Some wheels are going to be faster based off pf what they're made of, and others will turn more easily. However, the problem is, what happens when you have a combination of these? I think the best solution is to just take an average of the stats of all the wheels, and apply that as the stat for the TO at large. In other cases, they will have to be added up, as with the total mass supported per wheel.

As for spoked wheels, they would have to be a variant. This is a topic I have hinted at before but I will explain now. Certain FP's have multiple variants, which are unlocked under all the same circumstances, but have a different model and some different stats. There is a lot of potential in the future for this gameplay feature, but at the moment we will keep it limited. One example of this is the Blade FP. The two variants under the Blade are the Single-Edged Blade and the Double-Edged Blade. Before, these were their own FP's. Now, they're just variants of the same one. We should add that word into our dictionary, Variants.

For wheels, there would be three variants.

1. Wheel
   
2. Spoked Wheel
   
3. Tire
   

These three will have overall similar properties, but will differ in specific areas. Remember how earlier I said compounds will have a property that affects the stats of a wheel, and so that will be the determing factor of the wheel's stats? Well for consistency's sake, each individual compound will have the same effect on whichever variant it is used in.

Now, for creating these new properties that determine the affects- Wait a second, I just realized something. We don't have to create any new properties for the compounds. Its already covered by what we have!
Think about it. The lighter wheels, like wooden wheels or aluminum wheels, go faster but support less mass. The heavier wheels, like stone wheels, go slower but support more. What determines lightness or heaviness is density, which is already a property! When the density of the compound being used is lower, the wheel goes faster and turns faster, but supports less. When it is denser, it supports more but speeds less.

All we need to do is to create the equation. It would have to look something like this:
Wheel:

Mass_Supported = XY

Where X is the coefficient (a constant value) that will give us the most accurate result, and Y (the independent value) is the density of the compound being used.

So, we need to find the relationship between wheels and how much they can carry. Let's use wood as an example. After finding a trick on excel to take the average of all the recorded densities of wood, I got 576kg/m3 as the mean density of wood. I wouldn't say the Mass_Supported of a wooden wheel be 200kg. When you do the math it really screws up the numbers, and makes the Mass_Supported of iron wheels too high. I would say 50kg is more reasonable. So, we can plug that in and see what coefficient we get.

45kg = X(576kg/m3)
0.078 = X

Let's use iron as another example to see if we get similar results.
I would say around 600kg as the mass supported?

600kg = X(7870kg/m3)

X = 0.0076
Very close. If we were to settle on this number, than the final equation for the Mass_Supported of the "Wheel" Function Part would be:

Mass_Supported = 0.0077*Density

I will stop here, since it's getting quite late, but I want to hear some feedback. I think that if we base the stats of the wheels off of the compound's density and a certain coefficient in each case it would work. It would look something like:

Mass_Supported: A*d
Acceleration: B*d
Max_Velocity: C*d
Turn Time: D*d

With d being density of material used, and the other letters being the respective coefficients that we find.

I dont really agree with you. First of, the turning/max speed. When dealing with max speed, you generally want to reduce friction to the ground. However, when turning, you want to have that friction higher, because is the only causant of you turning. Finally, both acceleration and max speed actually depend much more of the engine and the total weight, and the wheel can at most set the cap.

Other than that, you wrote 0.0077 as the value of x, when it should be 0.077. However, i have a few arguments against that.

First of, it is not realistic. Lets say you want do do a wheel out of water. Wait, you shouldnt be able to. But your formula allows for it, and it would give us a wheel that can suport 77kg.

I would prefer if we added a few other variables to compounds so we can use anything other than density. Tension suported would be great for this, and for about half of the other FP.

Aditionally, all wheels (of the same material) are alowed to carry the same amount of weight, no matter their size. That is not too realistic.

Finally, i did an example. I took a locomotive (Big Boy) and ran it through your formula. I would assume that for multiple wheels, the total weight allowed is the sum of each wheel. It has a whooping 32 steel wheels, and a total mass of about 580000Kg loaded. That means that each wheel has to suport 18000Kg of weight. However, with your coeficient, each wheel would only accept 8000*0.077=616Kg, which is 30 times less than required.

Finally (again), if different wheels are used, the total weight suported should be the sum of each wheel, and as the other propierties are the caps, the final cap should be the most restrictive.

Also, I think we should use symmetry when placing down wheels. So every time you place a wheel on one side of the TO another symmetrical wheel would be placed on the other side. This would prevent players making TOs that would tip over.

Tarpy wrote:

Also, I think we should use symmetry when placing down wheels. So every time you place a wheel on one side of the TO another symmetrical wheel would be placed on the other side. This would prevent players making TOs that would tip over.

Suggestion: Pressing A would turn on asimetry, and pressing A againg would turn on simetry again.

No worries with the disagreement. I just wanted to get the discussion here going again.

Okay, so wheels set Mass Supported and Max Velocity.

For wheels out of water, I had realized that issue, but had yet to mention it. I was previously thinking that compounds have a tag assigned to them if they can't be used for wheels. However, if we introduce Tension Supported, then those other compounds wouldn't have to be worried about.

Oh, yeah, of course size would have to be factored into it as well. I had yet to get there. What would you propose?

That sounds good. Mass Supported is a sum of all the wheels. The most restrictive cap applies to all.

However, on the topic of the equation, what do you think it should look like?

@Tarpy and WilliamsTheJohn: Yup, the symmetry tool sounds good.

NickTheNick wrote:

No worries with the disagreement. I just wanted to get the discussion here going again.

Okay, so wheels set Mass Supported and Max Velocity.

For wheels out of water, I had realized that issue, but had yet to mention it. I was previously thinking that compounds have a tag assigned to them if they can't be used for wheels. However, if we introduce Tension Supported, then those other compounds wouldn't have to be worried about.

Oh, yeah, of course size would have to be factored into it as well. I had yet to get there. What would you propose?

That sounds good. Mass Supported is a sum of all the wheels. The most restrictive cap applies to all.

However, on the topic of the equation, what do you think it should look like?

@Tarpy and WilliamsTheJohn: Yup, the symmetry tool sounds good.

A large size of wheel increases mass supported, and decreases everything else?

Also, I'm calculating some more realistic coefficients.

I personally think that the symmetry tool would be automatic for the wheel and the player shouldn't be able to toggle the tool off in case of the wheel. The last thing we want to do is have to calculate momentum. Anyway, when was the last time you saw a vehicle with a wheel on one side and not another one on the other side?

(sorry for double post)

Anyways, here is a formula I have come up with:

Ms- Mass supported
Wn- Number of wheels on the TO
ρm- Density of the material
D- Diameter of the wheel

Ms=Wn*(ρm*D/10)

a- Average accelaration
F- The force exerted on the wheel via engines and other sources
m- Mass of the wheel
g- Average gravitational acceleration on the planet
frictionCoefficient- Self explanatory

a=(F-m*g*frictionCoefficient)/m

Tarpy wrote:

(sorry for double post)

Anyways, here is a formula I have come up with:

Ms- Mass supported
Wn- Number of wheels on the TO
ρm- Density of the material
D- Diameter of the wheel

Ms=Wn*(ρm*D/10)

I've got the formula:

Ms- Mass supported (in kilograms)
Wn- Number of wheels
ρm- Density of material (in tons per cubic meter)
R- Radius of wheel (in centimeters)

Ms = Wn * (ρm/8000) * 8.45^(0.0538 * R)

Decided through an analysis of the following four vehicles:
"Nissan Leaf"
"Union Pacific Big Boy"
"Stephenson's Rocket"
"Union Pacific 3985"

@Holomanga- Looks good to me. What do you think about the acceleration formula?

I would recommend someone try some examples with these equations and post what they get. I myself would like to but I am busy writing up some concept for the Strategy Mode.

Tarpy wrote:

I personally think that the symmetry tool would be automatic for the wheel and the player shouldn't be able to toggle the tool off in case of the wheel. The last thing we want to do is have to calculate momentum. Anyway, when was the last time you saw a vehicle with a wheel on one side and not another one on the other side?

I can think of two examples:

- A wheel right on the center. This should be handled by the symetry tool (attachments on the exact center will not have an opposite)

- A motorbike with a sidecar attached to it.

Actually, it is not too hard to determine if a vehicle is stable given an arbitrary number of wheels situated in arbitrary places. You only have to calculate the center of mass, project it to the ground, and see if it is in the area delimited by the places the weels touch the ground. If you are worried about calculating when vehicles would tip over (is it the right expresion?), we would have to do it for normal vehicles anyway, and it is something that the physic engine can do easily.

NickTheNick wrote:

@Tarpy and WilliamsTheJohn: Yup, the symmetry tool sounds good.

If these ideas are good enough, i think it would be good if someone puts them in TE current concept, and at wiki, at this shape:

All objects in TE will be symmetryc. To change it into asimmetryc, press A button, and to make it symmetryc again, pres A button again.

And it should go in controls list, to.

@Tarpy: The acceleration equation would be good here in reality, since it is basically a reiteration of Newton's second law, Fnet = m*a. However, in the game I don't think we would be calculating the friction of any possible patch of ground that the wheel would make contact with. I don't think friction would even be calculated at all. I think it would be better just to make wheels increase the MaxVelocity. Can someone get an equation for MaxVelocity?

@Holomanga: Very good mass_supported formula. As long as no one finds a problem with it, we can use it for the final concept.

@Daniferrito: So a variable symmetry tool then.

@WilliamsTheJohn: Not so fast cowboy. There's a lot left to discuss.

NickTheNick wrote:

@Tarpy: The acceleration equation would be good here in reality, since it is basically a reiteration of Newton's second law, Fnet = m*a. However, in the game I don't think we would be calculating the friction of any possible patch of ground that the wheel would make contact with. I don't think friction would even be calculated at all. I think it would be better just to make wheels increase the MaxVelocity. Can someone get an equation for MaxVelocity?

@Holomanga: Very good mass_supported formula. As long as no one finds a problem with it, we can use it for the final concept.

@Daniferrito: So a variable symmetry tool then.

@WilliamsTheJohn: Not so fast cowboy. There's a lot left to discuss.

Sounds good for me.

Holomanga wrote:

I've got the formula:

Ms- Mass supported (in kilograms)
Wn- Number of wheels
ρm- Density of material (in tons per cubic meter)
R- Radius of wheel (in centimeters)

Ms = Wn * (ρm/8000) * 8.45^(0.0538 * R)

Decided through an analysis of the following four vehicles:
"Nissan Leaf"
"Union Pacific Big Boy"
"Stephenson's Rocket"
"Union Pacific 3985"

No.

First of, we dont need Wn. we only need to calculate the weight for a single weel, and then we will add up the weight for each weel. However, it still gives us the same result, i just wanted to note it.

Second, i dont think using density is a good idea. It doesent relate to the real forces it can suport. Steel has roughly the same weight capacity of aluminium, but four times its density. That means that steel and aluminuim should have roughly the same weight capacity, but your formula assigns four times as much capacity to steel than aluminium. Gold is barely able to suport any forces, and would just be crushed under the weight of a vehicle, but your formula assigns it a weight capacity three times of that of steel. Something like tensile strength would be better, as wheels are definded by the tension of the material they are made of. There is a (rather ugly but usefull) table of materials on wikipedia: http://en.wikipedia.org/wiki/Tensile_strength#Typical_tensile_strengths

Third, the scaling with radius is wrong. It gives a quite small capacity to small wheels, and a humungusly large capacity to large wheels. For example, if you make a wheel with radius 500 (yes, that means a 10m tall wheel, bear with me) made out of steel, it would be able to suport 8.55944²⁴Kg. That is roughly the mass of the entire earth. On a single wheel.

Finally, the gravity should also affect it, althrough that is easy to fix. For a weight calculated on earh, just multiply the final value by *(g/9.8), where g is the gravity in m/s²

Tensile Strength sounds like a good property.

Could you show how you would model the equation?

Probably something like this:

Ms = (X*Ts*ln(Y*R+1))/g

Where:
Ms is the mass suported by an individual wheel (in Kg)
Ts is the tensile strength (in MPa), from the table
R is the radius (in meters)
g is the gravity of the planet (in m/s²)
And finally, X and Y are constants, which we can tweak to see what fits better.

That way, we have
Double the strength of a material, double the mass suported by a wheel made from it.
Double the gravity, half the mass suported.
When you increase size, the mass suported goes up, but eventually it is no longer usefull to increase size (a huge wheel eventually cannot suport its own weight)

My sugestions for X and Y are X=127.4, Y=0.06. However, my calculations are only based on the BigBoy locomotive again, so maybe the radius doesent escale well. That would mean that a 4 wooden-wheeled carromat would suport about 2800 Kg of weight, while the same carromat made out of graphene would suport about 9000000 Kg. We might want to lower that graphene value for our game, it is WAY too big.

Edit: Oh, just a few more numbers. The carromat from the example has a wheel radius of 0.5 m. Doubling that radius would make it able to suport 4000 Kg, while halving it would make it able to suport 1900 Kg.

That looks good, but could someone try out Dani's equation with further examples? I'll try some myself when I can get to it.

Also, I would agree that certain compounds be scaled back in their usefulness. Would we even include Graphene?

Okay, so when I used the equation it worked for me, using a car as an example. Since we've spent a long time on this FP, I propose we move to the next one, unless someone points out any mistakes soon.

Tarpy, be sure to put the description in the OP.

EDIT: Oh, actually, I just remembered. Can someone get an equation for max velocity? Wheels shouldn't be able to accelerate indefinitely.

NickTheNick wrote:

Okay, so when I used the equation it worked for me, using a car as an example. Since we've spent a long time on this FP, I propose we move to the next one, unless someone points out any mistakes soon.

Tarpy, be sure to put the description in the OP.

Consider it done. Also, instead of having max velocity and acceleration, we should just have average speed. Anyone else agrees on this?

Acceleration and max velocity are, in my opinion, pretty much too much of a hassle to program and just changing it to average speed would be easier.

There would still be problems like, e.g vehicles climbing steep ascends and going downhill. If everyone agrees with me on average velocity, we can then discuss the different modifiers on it.

To add up to my previous post, here is another reasons why I think acceleration and max velocity should be replaced with average speed :It would probably cause frame rate issues. First of all, the acceleration of a vehicle in vacuum, going on a perfectly smooth surface isn't the same as the acceleration of a vehicle climbing an 80 degree ascend in liquid mercury. We would have to calculate the acceleration of the vehicle every single time it enters a new type of environment. Not only that, but you won't have only 10 vehicles on your planet, you would have at least a hundred of them. When we calculate average speed, it would only change when the vehicle un-ignorably changes its location (from land to water).

I fully support just a value for speed instead of max speed and acceleration. It does make things a lot simpler.

If we are to adopt it, I have seen many RTS games where vehicles move slower or faster based on elevation without complex acceleration and max velocity equations, like in Men of War.

Here is my idea of the equation.

Total Average Speed = Average Speed x (1 - (Angle of Elevation/45))

A flat plain is 0 degrees angle of elevation, and a vertical wall is 90. Every increase in degree of the angle of elevation decreases the speed of vehicles, and vice versa. Would this be codeable? I'm thinking there might be issues for when the vehicle is not driving directly down or up a slope. Also, this equation allows negative angles of elevation, like when you are going down a slope. In such a case, you can get speeds higher than 100%.

Note the number in blue. Its assuming that vehicles cannot drive at a slope 45 degrees or greater. I was thinking that we could have new technologies increase this number, which would mean increasing the speed of vehicles on slopes and also increasing the max slope on which they could drive. Or we could just keep it static. Tell me what you think. Also, if anyone has a better equation, go right ahead. This is just for ideas.

Some technologies would increase the maximum angle the vehicle can climb upon, I agree with this.

Good formula, but we must also include the fact that the vehicle could be driving in water or mud or sand or snow etc. So, my formula would look like this (I have integrated your formula into it aswell):

Total speed=Average speed*(1-(Angle of Elevation)/45)*(Friction/(Mass of the vehicle/1000))

Friction would really represent the surface the vehicle is crossing. The values of friction would be as follows:

1.Dirt/Grass-1
2.Mud-0.6
3.Snow-0.9
4.Sand-0.7
5.Water-0.4

If the bolded part of my formula is larger than 10, than it will be equal to ten. The formula still needs a lot of revising. We should also agree on the Average speed value.

The problem is, how would we define what is dirt/grass? Where does it end?