Gear Ratios

[AlphaGnomeo]

For those who like to play around with gear ratios, here is an Excel spreadsheet (xls and xlsx) that you can use to show torque and horsepower information for various cars and transmission settings. (The data is for the 2009 CorvetteRM) Generally, the higher the total torque and HP, the better.

On page 1, you enter torque and HP data for the particular car. The resulting graph should match the GT5 graph.
On page 2, you enter the transmission settings that you want to use as a baseline.
On page 3, you can enter various gear ratios to see if they result in an improvement to the total torque/HP (the "area under the curve"). You can also enter various speeds for the track to see if the settings make sense for the track.

One challenge you will face is that on GT5, the gears that you can use are limited to a range. The top gear is determined by desired speed and final gear. I have not been able to figure out how GT5 computes the other gears for a particular speed and final gear setting. So you may have to go to GT5, find out the limits, input the values and see what happens.

Assuming that I have done the math right, this worksheet allows you to prove that some of the "tranny tricks" don't really work that well.

There are various improvements that one could make. For example, it does take drag into account. To address this, it might be helpful to include a place to input "required HP at various speeds", so that you can create a setting that maximizes HP when you need it most.

But give it a try and let me know if you find this helpful.

And let me know if you can figure out how GT5 computes the default gears and ranges. I have a fomula that generates results that are "almost" right (within a few hundredths), but I would rather have one that is 100% right.

Once I figure out how to insert images, I will add some screenshots.

 

[AlphaGnomeo]

I forgot to attach the files.

 

[dr_slump]

Wow! That looks great!

Thank you!👍👍

 

[TT3AZ]

And which formula do you use? Its this what you use:

peak torque*gear ratio*final gear?

Anyway going to check it out, thanks dawg.

File is corrupted....

 

[Basilea]

It looks very good... but a bit more explanation would be great.

A change in HP doesn't change the engine data at all?
And it stops computing the data at 7500 RPM a car with higher redline...
What does the Min. RPM on the tranny test page?


Thanks for the effort! Maybe you can unlock the excel file and others can work on it and might have some good changes or find a mistake in the math?

 

[No_OBsT33R]

Never hurts, I'm curious about the formulas used.

Looks good, but when I built my own version, I got stuck at the pre & post peek slopes + drop point. This info cannot be derived from the peek figures.

There are some "overrides" and "XY min, X max" stuff that I'm curious about.

Most importantly, how did you calculate the slope angle/ drop off points pre & post peek figures.

 

[TT3AZ]

I just want a calculator, that you can enter torque, rpm, gear ratio, and final drive. The calculator itself multiplies the torque with gear ratio and with final gear. That is tq*gear1*final gear = output torque. The tq for different rpm is estimates from the dyno graph, that i have made more detailed. I just want a program like this to compare different gear ratios, without make all the calculations manually.

 

[articzap]

That was really confusing and didn't show that my fastest gear set, was actually fastest.

hmmm?

 

[AlphaGnomeo]

I'm new to this forum, so I don't know how to do some of the basic things like attach pictures or reply to a specific post, so I will try to cover as many questions as I can.

On the last page, the MinRPM is the lowest RPM that you want the engine to run at. I then use a calculation that works backwards. The top gear is a simple calculation based on top speed, final gear, tire diameter, etc. The next gear down looks at the top gear and computes a ratio that tries to hit max rpm at the top gear MinRPM. The next gear does the same for the preceding gear etc. For various reasons, this does not always work out perfectly, so you sometimes have to vary the final gear or MinRPM to get a value that hits the MinRPM all the time. Anyways, it is only a suggested value and you can insert your own.

The worksheet is not limited to 7,500rpm. Just enter the engine data and it will expand all the way up to 13,000rpm in increments of 500.

The worksheet computes total "area under the curve" for torque and HP. My understanding is that the bigger this area, the better the gear set. But what is better really depends on "real world" conditions. For example, with respect to a particular track, it does you no good to waste 3 gears getting up to 60mph, when the lowest speed on the track is 80mph. This is why I provided for input of track speeds. Also, even though the formula should be better for maximizng straight line performance, there are limitations. For example, some generate such massive torque in lower gears, that the tires might lose traction. So there is probably a maximum value. Also, you do not want to waste your excess HP at lower speeds, but want to save it for higher speeds. That should be a fairly simple formula to graph, if anyone has examples of HP needed at various speeds.

Note that the "area under the curve" is an approximation, although a fairly close one. An exact calculation would yield exactly the same % change for total tor torque and HP, since the two numbers are interrelated. However, an exact calculation would require deteriming the formula that describes the torque, HP curve and then computing the integral of that formula.

I am not sure what effect changing the HP would have on the chart or on performance. I was mostly concerned about computing torque, because you can compute HP from torque. Changes in HP should change the HP chart. But, I am not sure what impact changes in HP have on the game. For example, if you put a HP limited on a car in the game, the torque should also change. But according to the charts it doesn't. And I am not sure whether GT5 uses torque or HP to compute "thrust".

I am including an "unprotected" version for those who want to check my math or try out enhancements. Just be careful not to overwrite a formula when inputting data.

 

[No_OBsT33R]

I'm new to this forum, so I don't know how to do some of the basic things like attach pictures or reply to a specific post, so I will try to cover as many questions as I can.

On the last page, the MinRPM is the lowest RPM that you want the engine to run at. I then use a calculation that works backwards. The top gear is a simple calculation based on top speed, final gear, tire diameter, etc. The next gear down looks at the top gear and computes a ratio that tries to hit max rpm at the top gear MinRPM. The next gear does the same for the preceding gear etc. For various reasons, this does not always work out perfectly, so you sometimes have to vary the final gear or MinRPM to get a value that hits the MinRPM all the time. Anyways, it is only a suggested value and you can insert your own.

The worksheet is not limited to 7,500rpm. Just enter the engine data and it will expand all the way up to 13,000rpm in increments of 500.

The worksheet computes total "area under the curve" for torque and HP. My understanding is that the bigger this area, the better the gear set. But what is better really depends on "real world" conditions. For example, with respect to a particular track, it does you no good to waste 3 gears getting up to 60mph, when the lowest speed on the track is 80mph. This is why I provided for input of track speeds. Also, even though the formula should be better for maximizng straight line performance, there are limitations. For example, some generate such massive torque in lower gears, that the tires might lose traction. So there is probably a maximum value. Also, you do not want to waste your excess HP at lower speeds, but want to save it for higher speeds. That should be a fairly simple formula to graph, if anyone has examples of HP needed at various speeds.

Note that the "area under the curve" is an approximation, although a fairly close one. An exact calculation would yield exactly the same % change for total tor torque and HP, since the two numbers are interrelated. However, an exact calculation would require deteriming the formula that describes the torque, HP curve and then computing the integral of that formula.

I am not sure what effect changing the HP would have on the chart or on performance. I was mostly concerned about computing torque, because you can compute HP from torque. Changes in HP should change the HP chart. But, I am not sure what impact changes in HP have on the game. For example, if you put a HP limited on a car in the game, the torque should also change. But according to the charts it doesn't. And I am not sure whether GT5 uses torque or HP to compute "thrust".

I am including an "unprotected" version for those who want to check my math or try out enhancements. Just be careful not to overwrite a formula when inputting data.

Thanks for including this. I was able to make my own power curve generator using peek numbers. The downward slopes are somewhat an estimate due to low detailed in game graph, but it's working well on a number of cars.

I'm hoping to save some time with shift point calculations with your spreadsheet.

Thanks again, many wouldn't go that far.

I'm new to Excel, but I've got the "Tables with Excel" book helping me along.

 

[AlphaGnomeo]

I listed the equations that I used on the spreadsheet.
You will find that about half of the content of the various Excel formulas are simply error detection or necessary to allow flexibility in the data fields.
For example, in any formulas that have if(xx = "","", etc.), you can ignore everything but the etc.
Feel free to disassemble the spreadsheet to make your own. That's how I learn any programming language - by borrowing, adapting and improving what others have done. The one thing you might have trouble moving are the graphs, since if you move them to a new spreadsheet, they like to refer back to the old spreadsheet. Also, note that the equations for the speed lines are hidden under the graphs to which they relate.

 

[shirakawaa]

The spreadsheet is good as a general guide, but doesn't take into account that in GT5 transmission losses affect driving torque delivery proportionally with rpm in each gear. In practice, this flattens slightly downwards thrust curves for each gear at higher rpm. This means that if at the flywheel (the chart you see in the tuning screen) power delivery was already somewhat flat at higher rpm, on the road it will go downwards.

Quick graphical example of the effect:

Abstract units. Orange = tq/pw at the flywheel; Green = tq/pw available in a gear on the road (total torque multiplication reduced to 1 for clarity)

In GT5, it's quite noticeable on cars with a flat power curve. You can feel that the optimal shift points are lower than what one would theoretically expect with tools such as your spreadsheet.

 

[No_OBsT33R]

I've been able to calculate the rate of resistance. This can provide the correction factor required. It takes a road test to properly calculate (it will also account for the rolling radius) I'll get it now.

So far I've got the power curve calculated

I've then use the power curve to create a graph for tq/rpm per gear, & a rpm shift calculator.

Just trying to tie the shift calculator in.

So far I can manipulate the shift rpm with gearing and rpm shift point per gear. However my rpm shift calculator doesn't connect directly to the graph indicating tq for rpm per gear. So I have to guesstimate tq levels after shift in new RPM by looking at the graph, but I'd like it to connect directly showing my shift points and rpm in the tq/rpm per gear graph for more precise calculations.

Any ideas?

I could post up my spreadsheet if it helps.

 

[No_OBsT33R]

Rolling radius - rolling resistance - aero resistance =

Gear * Final Drive / 0.00595 / (RPM/Speed)

Jump in your car, hit the track choose a gear and cruise at a given rpm & note the speed. Increase speed and note the new speed at a progressively higher rpm for the same gear. I suggest 5th or 6th to get the largest gap of speed for the widest range of results. The faster you go the more resistance.

Use the results in the formula and the progressive rate is the resistance.

 

[Basilea]

Well thanks again for the open file! I don't really understand why most don't give them to others? I know you put your work in it but if someone using it and can add or correvt things and shares it it would go a lot faster to get a good working gear ratio calculator for all!

 

[AlphaGnomeo]

SHIRAKAWA Akira, it looks like that would be a pretty easy variable to add to the equation. The estimates I have seen range from 15-18% loss for a manual transmission and 20-28% for an automatic. We could let the user insert his own variable and see what happens.

No_OBsT33R, what I was thinking would be most helpful would be to plot the required torque/hp for various speeds on the chart. This would automatically take into account the variables you mention, e.g., rolling friction, parasitic drag (including a coefficient of drag), etc. The result could be the sum of several formulae. Ideally, it would agree with your observational data. Or if it doesn't, we should be able to derive the numbers using observational data.

 

[No_OBsT33R]

My first run produced this

I'm going to crash, dig my head in further tomorrow.

Here is how my power curve looks on a Scoobie 22B

And gear power graph

More tomorrow.

 

[niky]

Better to reformat the gear power graph to show torque versus gear versus speed, as this is more useful for determining gear ratios for maximum acceleration and figuring proper shift points.

(This is from my own personal Excel file)

 

[No_OBsT33R]

Better to reformat the gear power graph to show torque versus gear versus speed, as this is more useful for determining gear ratios for maximum acceleration and figuring proper shift points.

(This is from my own personal Excel file)

That is sick.

I'm still new at excel, been messing around for a few weeks (note the rookie tables in my previous post) I'm still proud I got as far as I have.

I got the book on Tables today, but it's hard to find specifics to help.

How do I go about it from looking at what I've got so far?

Crap I got to work tomorrow, but

 

[niky]

Instead of doing a regular line chart, create an X,Y Chart. Then custom define the X,Y points by having a table arranged as so:

Torque in 1st / Speed in 1st, Torque in 2nd / Speed in 2nd, Torque in 3rd / Speed in 3rd...

A pain in the butt to do, and it takes forever, especially with the calculations involved, but well worth the time spent when it comes out looking so good.

 

[AlphaGnomeo]

No_OBsT33R, the formula for required HP is something like this:
HP = K x V^3
where:
V = speed in mph
K = k x Cd x A
where:
k is a constant that is supposed to take into account air density, gravity, rolling resistance. Examples given are 8.702 X 10^-6 or 6.7 X 10-6, where rolling resistance is added.
Cd = coefficient of drag, e.g. .33 on a Corvette
A = frontal area, e.g. 19 on a Corvette
Of course, we will never know the values that GT5 uses. But it looks like your test might be able to allow us to back into K for a particular car.
And, yes, in the Excel spreadsheet I used some lookup functions to compute the total values. Those are fairly complex and I don't use them much, so I have to hit the books to figure them out every time I use them.

niky, isn't that what my center graph on the last 2 pages shows? I don't have the dotted lines, but I do have the solid lines.

 

[No_OBsT33R]

Many thanks. I'm going to go over all of this, 2am and I work an early shift tomorrow. This is just too good.

This is the most helpful thread on the subject. A few great minds giving great info and real help. Thanks!

 

[shirakawaa]

SHIRAKAWA Akira, it looks like that would be a pretty easy variable to add to the equation. The estimates I have seen range from 15-18% loss for a manual transmission and 20-28% for an automatic. We could let the user insert his own variable and see what happens.

It isn't that simple. There are transmission losses dependant on vehicle speed and losses dependant on engine rpm (when a gear is engaged). Then there are tyre and aerodynamic losses. It isn't a single global percentage value (also, transmissions don't eat all that power. It's more like 8-10% for manual and 12-15% automatics, by taking out of transmission losses, tire losses).
Also, engine, transmission and wheel inertia can affect significantly shifting points in addition to acceleration. Theoretically, for example, with a very heavy flywheel you would have a greater acceleration in second gear than in first gear.

How do I know? Long time ago I made a quite complex spreadsheet similar to that featured in this thread, by which I could, with some sort of telemetry, measure my (or others') car's torque and power curves and graph various values.

This is a typical chart of an earlier version of my spreadsheet which didn't calculate inertia or losses in a complex way:

My conclusion after years trying to improve it has been that most of the time (as a driver who doesn't have access to technical data) there are too many unknown variables that add an unacceptable margin of error to "a priori" calculations of optimal shifting points. It's far simpler and safer to do that empirically by measuring acceleration directly in each gear (for example from 2000 rpm to the redline), then check at what speeds the acceleration curves meet each other.

 

[dr_slump]

I think another problem is when the power-/ torqueline don't cross themselves at 5250rpm.
This happens especially with the low and mid rpm turbo.

 

[Rotary Junkie]

I think another problem is when the power-/ torqueline don't cross themselves at 5250rpm.
This happens especially with the low and mid rpm turbo.

Scaling issue. Or rather, that GT tries to put torque and power on different scales so the top of the graph is where peak is for both.

 

[AlphaGnomeo]

SHIRAKAWA Akira, the "good" news is that we are not having to deal with the "real" world. We are dealing with the whatever world GT5 has created. And, based on what we have seen so far, I would expect that their calculations are fairly simplistic. And that is not because they want to be less realistic, but they probably see no point in spending cpu time modeling a lot of variables that affect speed and power by only a small percentage. For example, I would be amazed if GT5 modeled the effectis of change in air density due to weather or altitude - even though those can have a measurable impact on automotive performance in the real world.

 

[shirakawaa]

SHIRAKAWA Akira, the "good" news is that we are not having to deal with the "real" world. We are dealing with the whatever world GT5 has created. And, based on what we have seen so far, I would expect that their calculations are fairly simplistic. And that is not because they want to be less realistic, but they probably see no point in spending cpu time modeling a lot of variables that affect speed and power by only a small percentage. For example, I would be amazed if GT5 modeled the effectis of change in air density due to weather or altitude - even though those can have a measurable impact on automotive performance in the real world.

Those are not cpu-complex calculations at all (also, in case, with look-up tables there's no need to calculate everything in real-time). I believe PD have taken those data into account, as as time passed, top speeds/acceleration at high speed got more accurate compared to previous GT titles.
I still maintain that by using acceleration data directly (by logging for example with video camera on-screen car speed data) it would be easier to calculate optimal shift points for end-users like us.

 

[No_OBsT33R]

If we can calculate the rate of increased resistance with increased speed (as we can) is that not all the real time in game data we need?

At the shift point the resistance will be equal from one gear going in to the next. So all we would have to do is calculate the resistance level at the speed we are going when shifting, Both should be reduced by an equal percentage.

So for example (hypothetical numbers)

If shifting from 2 to 3 at 60mph while at 6000rpm drops you to 4000rpm in 3rd. The resistance is the same in 2nd @ 60mph @ 6000rpm as it is at 60mph @ 4000rpm in 3rd.

 

[AlphaGnomeo]

I still maintain that by using acceleration data directly (by logging for example with video camera on-screen car speed data) it would be easier to calculate optimal shift points for end-users like us.

I am hoping that there is at least some correlation between the computed results and the actual results. In the case of the Chapparal, the chart showed exactly why I was losing ground to my ghost self when I changed gear settings. I was faster in the places where it said I should be faster and slower in the places where it said I should be slower. Nothing more frustrating that watching your ghost self accelerate out of a corner faster.

Can data logger help in gathering data?

 

[AlphaGnomeo]

If we can calculate the rate of increased resistance with increased speed (as we can) is that not all the real time in game data we need?

I hate to say it is "all" we will need, but - at least in theory - it should be a large part.