Car's physics and setting...

reading here and there i found something. In first, in the Jonas notes, he wrote about wheels.friction is the friction caused by rotating the wheel in Newton metre.

So, I searched about calculating wheel friction and I found infos about rolling resistance, in which they explain:

F = Crr*Nf

where

F is the resistant force,
Crr is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF), and
Nf is the normal force.

They also give us a range for Crr: 0.030 to 0.035 for tires on tarmac.

Now I just needing Nf.

They provide (fortunately) a new example:

In a simple case such as a 40 kg object resting upon a table, the normal force on the object is equal but in opposite direction to the gravitational force applied on the object i.e. the weight of the object. In this case the normal force is given by, 40 kg · 9.81 m/s2=392.4 newtons where 9.81 m/s2 is equal to the acceleration due to gravity (near the Earth's surface).

In another case where the same object as mentioned above is on a 40 degree incline, we have to insert cos θ into the equation for normal force. Fnormal = mass · gravity · cos θ. So solving for the normal force, we get: FN = 40kg · 9.81m/s2 · cos 40° = 300.6 newtons

Now, I should able to calculate the friction. But, there is a big problem. The result is in [url=http://en.wikipedia.org/wiki/Newton_(unit)]newtons[/url], instead Newton metre. So, how convert the newtons in nm. And, we need to calculate the rim+tire weight, or including brake discs and other movement parts around the wheel?

in terms of weight, you would need to calculate the weight on the contact patch, i.e. car weight x weight distribution / 2 (i.e. one wheel per side). Basically, you need the corner weights of your car, which would include the tire, rim and brake disk.

For the rest, a force is always in Newton. On the other hand, Newton meter is always torque. So what jonas said doesn't make any sense to me, but I might just not understand it correctly.

Friction generally generates a force, as you wrote in your formula, never torque.

But then again, which friction are we talking about? Rolling resistance? Kinetic friction? Static friction? We have all three the tire/road contact patch, depending on the relative movement.

I've seen how wheel friction affects cars (for my slowest karts, I had to set wheels.friction to 0.01 for them to be able to get off the starting line at all). However, I didn't really bother messing around with the value on normal cars because it doesn't really affect the handling during racing. Still, it would be nice to compare our default value of 10/15 to some real life numbers.

During the Mythbusters Viewer's Special, their Crown Victoria coasted 2270 feet from 50mph. Let's try to replicate that inside Redline.

Car:
I took Redline's Crown Vic, changed the frontAirResistance to 0.74 (Wikipedia:8.7Cd-ft²), and I changed the finalDriveRatio to max out at 50mph. During testing, the wheels.friction was set to the same number for all four wheels.

Track: Default "new track" from Track Editor, finishPos-startPos=700m (2300ft), startLineOffset 100m to allow for accelleration to 50mph

Testing:
Accellerate to top speed 50mph, as soon you cross the starting line, throw the car into neutral (important! this removes engine friction). Perform further testing by modifying wheels.friction until the car crosses the finish line at around 1mph.

Result:
wheels.friction 53 (!) for each wheel, top speed 50mph, avg. speed 26mph, time: 1min07sec (700m+100m)
Perhaps the high result is because Redline doesn't have friction for the transmission, so wheels.friction needs to be higher than the 15Nm per wheel that maybe Jonas found somewhere.

It seems that our values are too low, but it shouldn't matter very much. The only situations where wheels.friction should be important is during coasting at low speeds, where there's no engine friction and very little wind resistance.

Getting frustrated by the dodgy suspension, I've tried to provide some measured data for the effect that wheels.maxsuspension has on the bump frequency and compression time (time from resting position until full compression).

Testing vehicle had mass = 1000 (irrelevant), CoG placed at {0,0,0}, supsensionFriction = 0, damperStrength = 0, frontSwayBar & rearSwayBar = 0. I also had to set topAirResistance = 0 so that the car could bounce around for a whole minute, which was my observation window. I know that these settings are not something you would have in a normal car, but I'm just trying to isolate the variables here.

Wheels.maxSuspension	Bounces/min	Frequency	Compression time (λ/2)	Response time (λ/4)
1.00 m	43	0.72 Hz	0.698 s	0.349 s
0.500 m	61	1.02 Hz	0.492 s	0.246 s
0.250 m	86	1.43 Hz	0.349 s	0.174 s
0.200 m	96	1.60 Hz	0.313 s	0.156 s
0.180 m	101	1.68 Hz	0.297 s	0.149 s
0.160 m	107	1.78 Hz	0.280 s	0.140 s
0.140 m	115	1.92 Hz	0.261 s	0.130 s
0.125 m	122	2.03 Hz	0.246 s	0.123 s
0.100 m	136	2.26 Hz	0.221 s	0.110 s
0.080 m	152	2.53 Hz	0.197 s	0.099 s
0.060 m	172	2.86 Hz	0.174 s	0.087 s
0.040 m	207	3.45 Hz	0.145 s	0.072 s
0.020 m	322	5.37 Hz	0.093 s	0.047 s

From the data in the table above, we see a rather linear relationship between wheels.maxSuspension and the compression time. However, when the suspension travel becomes 0.1 or less, the curve steepens dramatically. My guess is that these lower values are challenging the time resolution of the physics engine, causing imprecise results. I tried to get a reading for a suspension travel of 0.01, but it was too quick to determine what made up a suspension cycle with Snapz Pro X recording at 25 fps. Values <0.01 causes the car to become nervous and flip over. Negative values work - the wheels bounce below the surface, and Redline introduces it's very own soft emergency suspension, making cars look like jumping animals (at least with zero damping).

I found a mathematical relationship in the numbers above!

For every time wheel.maxSuspension is reduced to half the distance, the frequency is divided by 1.41, or (I guess this is a correct assumption) the square root of 2. I'm also assuming that the formula centers around the instance of "1Hz@0.5m", where the 0.5m value is 2*wheels.maxSuspension. It's a value also used when the calculating the resting height of the car, so I'm taking the chance that this is the variable that the physics engine also calculates the suspension frequency from. With these assumptions, we can arrive at a formula to calculate the natural suspension frequency:

f_natural = sqrt(2*wheels.maxSuspension)

By the way, suspensionFriction and damperStrength data is on its way... it's worth the wait.

I can't wait!

That maxSuspension algebra above involved using binary logarithms (which I hadn't done since high school), so my head is spinning a bit at the moment. Here's what I have so far that describes the other suspension variables.

I'm trying to find a way to calculate the following variables:
(suggestions for better variable naming won't hurt)

CTR -- cycles to rest -- the number of full suspension movement cycles until the suspension is stationary at its resting position.
t_c -- compression time / half-cycle-time -- the time it takes for the suspension to move from one extreme to the other. From extended->compressed or compressed->extended
t_r -- response time -- the initial time it takes for the suspension to move from it's first extreme to its resting position. The relationship between this and the compression time can give us a damping curve.

other variables:
m: mass
s_max: maxSuspension
s_f: supsensionFriction
s_d: damperStrength

I'm keeping sway bars out of the picture, they're all set to 0 for now. For those of you who want to know - sway bars under pressure reduce load transfer at the cost of reducing suspension travel. So yes, they are involved, but I'm not doing the number crunching for that.

Anyway, here's a couple of relationships that I've figured out from my test data:

1) CTR_f, or the number of cycles to rest that you get by only using supsensionFriction, is linearly proportional to mass.
CTR_f = 2*m / s_f
Example: A car weighing 1500kg will need a supsensionFriction of 3000 to complete 1 cycle by only using supsensionFriction. To keep the same amount of cycles, modify the supsensionFriction by the same factor that you modify the mass with.

2) CTR is most likely a sum of the resistance in "the springs and the dampers", and not a product of the two.
CTR = CTR_f + CTR_d
This is unconfirmed, so I'll need to test with combining a positive and a negative value to see what the result is.

3) CTR_d follows the same relationship to mass as the supsensionFriction, but speed (and therefore wheel.maxSuspension) plays a part that I have yet to determine.

I have lots of data, but I'll try to get the last two points sorted out before I share them with you. After that, we'll see if we can find a way to calculate both the compression time and response time.

I'm reading wikipedia's article on damping - I didn't study it in my two first year physics courses, though the DEs look familiar enough from later math courses.

Solving for time seems like it might be tricky, given where it shows up in the solutions to the DE:

x(t) = Ae^{y + t} + Be^{y - t}

(A, B, are determined by the starting conditions, and y is a function of the spring and damping coefficients and mass)


--

If CTR_f is a linear relationship between suspension friction and math, if you set it to be 0.5 cycles (ie, suspension friction equals four times the car's mass), does the car really return to rest with no oscillation of the suspension? If so, you could probably use that to set up a simpler equation to figure out the spring rate (which Jonas has said is calculated):

1 = c_damping / ( 2 * √ ( k * m ) )
=>
k = ( c_damping / 2 )² / m
= c_damping² / 4m

NoNameBrand wrote:If CTR_f is a linear relationship between suspension friction and math, if you set it to be 0.5 cycles (ie, suspension friction equals four times the car's mass), does the car really return to rest with no oscillation of the suspension?

damperStrength behaves in this way, reducing the amplitude until 0. The behavior is different with supsensionFriction, where the springs go slower and slower until they stop. For instance, if I set it up to stop at 0.5 cycles, the initial response takes very little time, while the rebound phase (0.25-0.5 cycles) takes 5-10 seconds. Difficult to measure.

If it turns out to be too difficult to find a formula for calculating the times, I'll at least provide a data table with reference values.

I hope you don't mind the space that these tables occupy...

Different supsensionFriction at mass 1000, wheels.maxSuspension 1.0:

supsensionFriction (sf)	Cycles-to-rest (CTRf)	Response time (tr)	Compression time (tc)
0	infinite	0.33 s	0.67 s
100	22	0.33 s	0.67 s
200	11
300	8
400	6
500	5
600	4.25
700	3.5
800	3
900	2.5	0.33 s	0.67 s
1000	2.25	0.37 s	0.67 s
1200	2	0.37 s	0.67 s
1600	1.75
2000	1.5	0.37 s	0.67 s
2400	1	0.40 s	0.73 s
3000	<1	0.40 s	0.77 s
3500	0.75	0.43 s	0.77 s
4000	>0.5	0.47 s	0.73 s
4500	>0.5	0.5 s	0.67 s
5000	0.5	0.6 s	0.6 s
6000	<0.5	4 s	4 s
8000	<0.5	8 s	8 s
10000	<0.5	>10 s	>10 s

Comments:
- Compression time can be ignored for all stiffnesses that result in 0.5 cycles or more, as it's roughly equal to the natural frequency of the suspension (0.7 in our test case with 1m travel)
- Once you reach less than 1 cycle to rest, the response time approaches the compression time
- As mentioned before, the last movement until the suspension rests is very slooow, and that also makes some results quite difficult to measure.
- Once the cycles to rest is less than 0.5, the suspension moves rather quickly for a short distance (90% @ s_f=6000, 20% @ 10000) before it starts it slow settling process.
- While the curve is linear for the most part, there is an offset compared to the formula I gave earlier. That formula assumes that the magic values for supsensionFriction are multiples of 2000, while my data suggests that multiples of 2500. I don't know if this is just a result of the inaccuracies of my measurements, or if the difference is so great that it should be shown in the formula. Alternative formula with the new constant: CTR_f = 2.5*m / s_f


Different masses at supsensionFriction 2400:

mass (m)	Cycles-to-rest (CTRf)
500	0.5
1000	1
2000	2
3000	3
4000	4
5000	4.5

Comments: The relationship seems to be linear.


Different damperStrength at mass 1000, wheels.maxSuspension 1.0:

damperStrength (sd)	Cycles-to-rest (CTRf)	Response time (tr)	Compression time (tc)
100	>30	0.3 s	0.67 s
200	>30
300	20
400	15
500	12
600	10
700	8
800	7
900	7
1000	6
1250	5.5	0.36 s	0.7 s
1500	4.5
1750	4
2000	3.5	0.36 s	0.73 s
2500	3	0.40 s	0.77 s
3000	2.5	0.40 s	0.77 s
3500	2
4000	1.5	0.47 s	0.80 s
4500	1.25	0.5 s	0.80 s
5000	1	0.5 s	0.90 s
6000	0.5	0.63 s
6500	0.5	0.67 s
7500	0.25	0.8 s	0.90 s
8750	0.25	1.07 s
10000		1.27 s
11250		1.5 s
12500		1.73 s
15000		2.03 s	2.03 s
17500		2.37 s
20000		2.53 s
22500		3.1 s
25000	0.25	3.43 s	3.43 s

Comments:
- Similar to supsensionFriction (2500 -> 1), damperStrength seems to be based on the number 5000. Since damperStrength depends on speed, it has a similar pattern to the one we found for wheels.maxSuspension: If the damperStrength is reduced by a factor of the square root of two, the number of cycles to rest is multiplied by two. Arriving at the wheels.maxSuspension formula was difficult, so I'll have to look at this formula later on.
- Once damperStrength is strong enough to result in 0.25 cycles to rest, it doesn't "dampen just a short bit and then take time to settle" like supsensionFriction, but rather just smoothly dampens at a steadily growing rate. I don't plan on figuring out this rate, as I imagine most of us don't want such behavior in a car. The exception could be if you were making a hovercraft of some sort.


Tables for damperStrength with different mass and with different wheels.maxSuspension will have to wait a bit, I'm having a bit of a hard time reading good results from my tests.

C14ru5 wrote:
- Once damperStrength is strong enough to result in 0.25 cycles to rest, it doesn't "dampen just a short bit and then take time to settle" like supsensionFriction, but rather just smoothly dampens at a steadily growing rate. I don't plan on figuring out this rate, as I imagine most of us don't want such behavior in a car. The exception could be if you were making a hovercraft of some sort.

Funny enough, all my cars have damperStrength set to more than 7500.

No need to worry, remember that this is data for 1m suspension travel.

in quite addicted by your calculations, im not posting just for avoiding interruptions, but its time for me to understand one thing.

I suppose, these tables and your efforts will be really useful for supsentionfriction and damperstrenght. But what I missing is: you wrote about the time to rest of suspension based on travel and car mass. But It will be proportionally for all cars, or we need to use these table as just a starting point?

es:I have 2 BMW. They both have a suspension travel of 0,12 meters. But in the first one, the carmaker decided to have stiffer suspension, in the second one a suspension aimed for comfort. How I can extract this example from these tables?

DonaemouS wrote:But It will be proportionally for all cars, or we need to use these table as just a starting point?

It should be proportional, we just need to be sure about how it's proportional.

DonaemouS wrote:es:I have 2 BMW. They both have a suspension travel of 0,12 meters. But in the first one, the carmaker decided to have stiffer suspension, in the second one a suspension aimed for comfort. How I can extract this example from these tables?

To be honest, I don't know yet.

Different masses at damperStrength 1750, wheels.maxSuspension 1.0:

mass (m)	Cycles-to-rest (CTRd)
250 kg	0.5
350 kg	1
500 kg	1.5
700 kg	2
850 kg	3
1000 kg	4
1400 kg	6
2000 kg	8
2800 kg	12
4000 kg	16
5600 kg	24
8000 kg	24? 32?

Comments: The relationship seems to be linear for 1000 kg and above, but not for values below 1000 kg. I have no idea if this has to do with poor measurements on my side, or if there's a precision problem similar to what we saw with how low values for wheels.maxSuspension would give higher natural suspension frequencies than the formula.


Different wheels.maxSuspension at damperStrength 2500, mass 1000:

wheels.maxSuspension (smax)	Cycles-to-rest (CTRd)
0.0625 m	8?
0.125 m	8
0.25 m	6?
0.5 m	4
1.0 m	3
2 m	2

Comments: It's really hard to get data when it's on such a small scale, I had to use to use "allCams 1" and "finger-on-screen", and even then there was a lot of guessing. Let's look at some data at the other end of the scale, and see if we can spot a pattern...

Different wheels.maxSuspension at damperStrength 625, mass 1000:

wheels.maxSuspension (smax)	Cycles-to-rest (CTRd)
0.5 m	>16
1 m	12
2 m	8
4 m	6
8 m	4
16 m	3

Comments:
- These numbers look very clean, but I admit that I don't see the pattern. However, the behavior is very similar to the table above with the numbers belonging to the shorter suspension travel
- Mass and wheels.maxSuspension affect CTR in opposite ways. Hard to say if they're inversely proportional, though.


This work makes me wish that I had the code in front of me
It also wouldn't hurt to receive help from a mathematician.

It also wouldn't hurt to receive help from a mathematician.

log vs log might help you find a linear relationship...

I'm just at the wrong computer right now, will edit this later.

C14ru5 wrote:Different wheels.maxSuspension at damperStrength 625, mass 1000:

wheels.maxSuspension (smax)	log2 smax	Cycles-to-rest (CTRd)	log2
0.5 m	-1	>16
1 m	0	12
2 m	1	8
4 m	2	6
8 m	3	4
16 m	4	3

Zing! Spring constant!

At equilibrium, m * g = -k * x.

m = mass of the car * front-rear weight distribution / 2
x = maxSuspension / 2
k = spring constant, which redline calculates.

Let's take a hypothetical car with 50/50 FR distribution that has a mass of 1000kg, and a suspension travel of 0.1m at each corner:

250kg * -9.81 m/s² = -k * 0.05m
k = 250kg * 9.81 m/s² / 0.05m = 49050 N/m

How this helps: we can calculate this value for each sample of C14ru5's data (need to know how far the test wheel was from the CoM), and reduce the number of unknowns to the damping coefficient, and try to figure out how that's calculated from the .car parameters.

Im reading this with one eye and can get over how damn smart you guys are. Lucky thing I was cute when I was young!

indeed....what seeflat said. it all looks like swahili to me. i wasnt that cute, so i had to fight my way out.

thanks all for the effort. i wouldnt be here if it wasnt for you. slow

NoNameBrand wrote:need to know how far the test wheel was from the CoM

CoM was at {0,0,0}, which isn't relative to the ground, but to the resting height of the wheels at {1,0,1}, {-1,0,1}, {1,0,-1}, {-1,0,-1} (for instance, the wheels.pos height in the .car was 0.5 m for 1m travel)

I have one more test to complete, and that's combining positive and negative values of supsensionFriction and damperStrength to see if this affects response time and can be used to get around the stiffness/travel limit given in wheels.maxSuspension. I doubt I'll have any time to do it this weekend, but I'll try it sometime next week.