Total Power Calculation over gears/speeds

[GhostZ]

So I've been playing around with numbers again.

Does anyone know, with any accuracy, how PD comes up with the formulas for their torque curves for cars, and how they are changed when certain upgrades are bought?

 

[praiano63]

So I've been playing around with numbers again.

Does anyone know, with any accuracy, how PD comes up with the formulas for their torque curves for cars, and how they are changed when certain upgrades are bought?

No idea about what or how PD is doing all this calculation. I think even themself are a little bit lost lately.

But i've found in a french site an explanation about torque and power that is clear and easy to understand.
Just need to convert Ft/lb in N m and RPM in rad/s

here is it , from this link. http://www.gt5rs.com/post302026.html

The torque is the force given by the engine.

Power, it is conditioned by the torque and the rotation speed of the motor according to the simple formula: P = V * C (C being the torque (Nm) and V its speed (in rad / s) )

So we can say that a little engine that have a low torque but who can turn very quickly, could provide the same power than the engine who is turning slowly and providing a monster torque.

This is why a car engine is often designated by its power. However, as can often be seen, the max torque is not the same rpm as the maximum power.

A small example:

Mercedes-Benz A 160 Avantgarde '98 original developped a maximum torque of 149.94Nm a 4000 rev / min. (4000rpm = 418.87904 rad / s)

P = C * V
P = 149.94 * 418.87 = 62806.87 W = 85.34 c.

However, a 5250 rev / min (approximately 549 rad / s) it develloppe 102 hp (or 75 072 W)
By the inverse operation, it is

C = P / V
C = 75072/549 (rad / s) = 136 Nm

We see that the torque is a lower 5250 rpm / min, but the engine is more powerful.

I can understand this more or less now, i'm not good at all with this but i think it can help somebody who like to play with this .

><(((((°>°°°°°°/

 

[esoxhntr]

I suspect (and would hope) PD gets their torque / power curves from actual dyno graphs from the manufacturers.

another way of looking at praiano's formula is:

HP = (TORQUE * rpm) / 5252
or
TORQUE = (HP * 5252) / rpm

so

a car with 300lbft of torque at 5000 rpm generates 285.6 HP at 5000 rpm

a car with 400 hp at 7000 rpm has 300lbft of torque at 7000 rpm

5252 rpms is a magic number when it comes to engines. It is the point where torque and HP cross or are equal. no exceptions. below 5252 rpms torque will ALWAYS be higher, above HP will ALWAYS be higher.

 

[praiano63]

I suspect (and would hope) PD gets their torque / power curves from actual dyno graphs from the manufacturers.

another way of looking at praiano's formula is:

HP = (TORQUE * rpm) / 5252
or
TORQUE = (HP * 5252) / rpm

so

a car with 300lbft of torque at 5000 rpm generates 285.6 HP at 5000 rpm

a car with 400 hp at 7000 rpm has 300lbft of torque at 7000 rpm

5252 rpms is a magic number when it comes to engines. It is the point where torque and HP cross or are equal. no exceptions. below 5252 rpms torque will ALWAYS be higher, above HP will ALWAYS be higher.

This is not my formula ... But it's more clear and simple this way. Magic numbers.... Thanks for this.

 

[Adrenaline]

I don't think the graphs are from real dynos, based on the simple observation that they don't intersect at 5252.

 

[praiano63]

I don't think the graphs are from real dynos, based on the simple observation that they don't intersect at 5252.

When you check power x torque curves on the net , it never cross at 5252.
I don't think it's what esoxhntr wanted to say.
But in the game, if you make match torque and HP like i did with hte pontiac GTO,
the max power go to 5600 rpm
and the torque go to 4700 rpm

5600-4700=900/2=450+4700= 5150 !!! Bingo ?? or not Bingo ???.

 

[esoxhntr]

Adrenaline: The scale of the HP curve is not the same as the TQ curve on the PD graphs, if that makes sense [another PD blunder IMO]. Hence they don't cross where you'd guesstimate 5252 to be.

But they do.

It's plain to see on praiano's example above. if you moved the torque curve up so that graphically the peak of 613 is at the samel level as the hp peak of 613 you'd be a little closer or maybe bang on. i'd guesstimate 595 hp / torque at 5252 for that car.

Praiano, you are assuming the HP curve is linear (rises at the same rate) between 4700 and 5500. But it rarely is. But your figure of 5150 is pretty close

 

[GhostZ]

I already know how to convert torque to HP, I want to know a function formula to come up with torque curves. I want to estimate the curves and take the integral of the power band, multiplied by all of the gears, to give me exact torque numbers for the car over its entire gear, or (if there's no wheelspin) from a given speed to another speed. I can then tune to maximize that, and (theoretically) even make up a formula that gives the most advantageous gear ratios for a set of speeds, that results in the most torque on the ground with just the right amount of wheel slip.

Also, 5252 is an approximate number (the real number is some decimal after that) of when power and torque are equal for American Horsepower, and standard Ft/lbs of torque. If you're using BHP, PS, or any other torque unit, it's going to be a different formula.

@Praiano: Not bingo. Your figured out the halfway point between peak HP and peak torque, which is not at all the same as where they cross, since the curves are not lines but have varying slopes. Torque doesn't have to drop down after they cross, look at an F1 engine graph (or most hondas) for an extreme example. Torque still rises after 5252, but HP is rising at a higher rate at that point and crosses it. If you did your calculation, you would say that F1 engine's torque and HP cross at near 15000 or 16000 RPM, which isn't true at all. They'd need to be making nearly 800 ft/lbs to reach those power levels, if HP and Torque were equal at that RPM!

I've already got one that, using production numbers of max torque and peak power at various RPMs was able to simulate the torque curves of a number of N/A engines (Nissan L28, Chevy LS2, 4A-GE, Dodge 413 Max Wedge) with some degree of accuracy) but if someone knew how PD actually figures it out it would help me a lot.

Edit: Esoxhntr beat me to it. Yeah, there's a scale problem as well on PD's graphs.

 

[Rotary Junkie]

I don't think the graphs are from real dynos, based on the simple observation that they don't intersect at 5252.

They don't intersect at 5252 because the scale isn't equal and/or the scale is based on something other than HP and ft/lb.

As for what you're trying to figure out GhostZ... Well... I can't tell you. I can tell you that the only modifications that actually change the shape of the curve are forced induction mods (the 3 turbo stages or a supercharger), and that engine tuning stages, exhaust/muffler (not manifold), race cat, and the ECU all increase the rev limiter and stretch the powerband to match it. I'd be willing to bet it's all % changes for a certain % area of the RPM band.

 

[esoxhntr]

GhostZ, you really can't come up with a bulletproof formula. PD has not given us enough info. We have two reference points torque at max torque, and torque at Max Power (via formula), we also have the same two points for HP one via formula. We also know they cross at 5252. From those three points you *could* plot a graph that will get you "close" but it assumes that power rises / falls in a linear fashion between them.

 

[GhostZ]

It's not a "bulletproof" formula, just an estimation. It's a few translations on a x-cubed graph so that if I know peak torque, rpm of that peak torque, how much torque the engine makes before entering its powerband, and the length of the powerband, (all variables in the formula you can play around with) you can mess with the shape until you get a shape that has a corresponding power curve that matches OEM numbers. The problem is that it is fairly generalized. While I would say it is very accurate for, say, for most N/A engines, it isn't for a motor with highly peaked torque curves, or the mess that is the Ferrari F430 Scuderia or S15 silvia torque curves might be more difficult to fit.

Power doesn't have to fall linearly at all for us to be able to fit a line. Hell, power could bounce up and down all of the way to redline and there is still some graph formula that could replicate it.

My next thought was using a piece-wise function on a case-by-case basis to simplify the graph of any cars I can't do with the regular formula.

 

[bread82]

@ GhostZ: Another option you could try, rather than trying to mimic the power curve through a formula (which as you said above is generic and thus would be hard/time consuming to fit to different cars), is using some graph digitisation software to plot the graphs from GT5, or RL dyno printouts, in a usable form.

I used something at work called "Grab It!" (there must be other programs out there) which appeared to be an Excel sheet with a load of macros bolted on. The trouble is I only had a freeware version and it either didn't have everything enabled or was buggy, so I was unable to get any output from it.

The basic idea is you get a pic of your graph (phone camera snap from the GT5 setings screen I guess), then import it to the program. You define axes limits by clicking on them and labelling (so 0 to 8000 rpm, 0 to 200 lb.ft or whatever), then it converts the line to a load of (x,y) coordinates. You could then put these coords into a normal excel sheet and fit whatever function you liked to it. Get this function, integrate between the limits you want to set (rpm upon shifting up to the gear, redline), should be job done.

Looks like you're going for the "high peak horsepower sells cars, high average horsepower wins races" approach 👍

I think that some of the GTRs' (and maybe other) curves in GT5 are weird. The power and tq peaks say one thing in the written panel, but the images show something different, like easily 1000 rpm different.

Scarcely related anecdote - I work in a lab, once we needed a quick fix to get an area under a curve that had come from a printout. Option 1 was to print it on squared paper and count the squares, which was the sort of thing we did at primary school and would have taken a while. Option 2, which worked very well was to print on normal paper, cut out the curve and weigh the section on a microbalance. We knew the gsm and dimensions of the A4 paper and could therefore scale our cutout from this. I LOLed when this was suggested but it was actually very accurate.

Cheers,

Bread

 

[dr_slump]

They don't intersect at 5252 because the scale isn't equal and/or the scale is based on something other than HP and ft/lb.

The second

Go and change the used units by switching between system languages, you'll notice that even with different units the graphs stay the same.

 

[GhostZ]

@ GhostZ: Another option you could try, rather than trying to mimic the power curve through a formula (which as you said above is generic and thus would be hard/time consuming to fit to different cars), is using some graph digitisation software to plot the graphs from GT5, or RL dyno printouts, in a usable form.

I used something at work called "Grab It!" (there must be other programs out there) which appeared to be an Excel sheet with a load of macros bolted on. The trouble is I only had a freeware version and it either didn't have everything enabled or was buggy, so I was unable to get any output from it.

The basic idea is you get a pic of your graph (phone camera snap from the GT5 setings screen I guess), then import it to the program. You define axes limits by clicking on them and labelling (so 0 to 8000 rpm, 0 to 200 lb.ft or whatever), then it converts the line to a load of (x,y) coordinates. You could then put these coords into a normal excel sheet and fit whatever function you liked to it. Get this function, integrate between the limits you want to set (rpm upon shifting up to the gear, redline), should be job done.

Looks like you're going for the "high peak horsepower sells cars, high average horsepower wins races" approach 👍

I think that some of the GTRs' (and maybe other) curves in GT5 are weird. The power and tq peaks say one thing in the written panel, but the images show something different, like easily 1000 rpm different.

Scarcely related anecdote - I work in a lab, once we needed a quick fix to get an area under a curve that had come from a printout. Option 1 was to print it on squared paper and count the squares, which was the sort of thing we did at primary school and would have taken a while. Option 2, which worked very well was to print on normal paper, cut out the curve and weigh the section on a microbalance. We knew the gsm and dimensions of the A4 paper and could therefore scale our cutout from this. I LOLed when this was suggested but it was actually very accurate.

Cheers,

Bread

This is brilliant. Excellent help. I think I got a good idea what to do now.

 

[bread82]

@Ghost: No problem, hope it works for you. If you find any decent graph software I'd be interested to know. Perhaps the same approach could be applied to the data logger for longitudinal G? It might be interesting to calc tyre force on the road from the acceleration of the car; the peak long' G can be found through the SSRX speed test to potentially calibrate the axis in the data logger. Kind of approaching the problem from the effect rather than the cause?!

I wonder if the two approaches would agree with each other. It could be interesting if they don't. Specifically - I don't know if the dyno graph in GT is meant to be at the wheels or crank, (or how accurate it is). Accel of the car body (long' G) could also be affected by the springs squatting on launch? One for the drag forum I guess.

I can tell you that the only modifications that actually change the shape of the curve are forced induction mods (the 3 turbo stages or a supercharger), and that engine tuning stages, exhaust/muffler (not manifold), race cat, and the ECU all increase the rev limiter and stretch the powerband to match it. I'd be willing to bet it's all % changes for a certain % area of the RPM band.

Agreed. It's a shame that GT doesn't have more in-depth NA tuning:tdown:. The blurb for NA+3 even mentions a cam swap - this is obviously not reflected in the power band! Since turbo lag *nb: lag=spool time, not boost threshold - these terms have caused confusion in other threads* isn't implemented in GT5 it kind of feels like the turbo upgrades are equivalent to a big increase in compression ratio (more power across the board), and cam swap (favouring a specific rev range). Would be nice if GT had high compression pistons: +1,2,3, and cam: mild, medium, aggressive. I've not played Forza but the cam and valve upgrades do look interesting.

Ghost do you also play Forza? The youtube videos of telemetry I've seen look pretty in-depth. If you like number crunching there's probably loads to mess around with.

Cheers,

Bread

 

[GhostZ]

I assume GT5 graphs are at the crank, with full accessories since they tend to match OEM numbers for the US cars (which use that same approach). Likewise, I believe that changing drivetrain parts on some cars can change driveline Resistance. I heard somewhere a while ago that for cars like the McLaren F1, the stock transmission puts more power at the wheels for the same gear ratios down than the tunable ones for this reason.

Unfortunately I do not play Forza, but I do agree that more detail to statistics and options needs to be done in GT5. Particularly individual engines which have massive variety in their uses and tuning in real life, and many more options than just single types of engine upgrades.

I would also love to see fuel types introduced, and fuel regulations. But that's a whole different ballgame.

 

[brianwong]

I assume GT5 graphs are at the crank, with full accessories since they tend to match OEM numbers for the US cars (which use that same approach). Likewise, I believe that changing drivetrain parts on some cars can change driveline Resistance. I heard somewhere a while ago that for cars like the McLaren F1, the stock transmission puts more power at the wheels for the same gear ratios down than the tunable ones for this reason.

Unfortunately I do not play Forza, but I do agree that more detail to statistics and options needs to be done in GT5. Particularly individual engines which have massive variety in their uses and tuning in real life, and many more options than just single types of engine upgrades.

I would also love to see fuel types introduced, and fuel regulations. But that's a whole different ballgame.

I remember GT4 used to have different engine tuning than just "1 2 3" and there were actual explanations for the weight reduction.