How to calculate max velocity of a vehicle from torque and RPM?

[dehseth]

Hey guys,

I'm kinda simulate vehicle dynamics. I got gear ratios, torque and RPM values. I find how to calculate instant accerelation from
http://spreadsheets.google.com/ccc?key=pBCH2ClzmrplHUNFgrkT7HA

Ok now I got acc. I can calculate velocity from acc but my problem is how to calculate losses. I cannot constantly increase vehicle's speed. At certain speed it will stabilize and won't increase or decrease if I keep car's RPM constant... So basically I need to calculate max velocity of a vehicle at instant RPM and torque...

Thank you all..

 

[xxChrisxx]

Losses aren't trivial to model.

You will likely have to specify them. Drag and rolling resistance will be your main components. For that you need to know nothing about the engine, but the car/vehichle itsself. If you want to incluse drive train losses, you will have to specify them. These will most likely be rule of thumb estimates. Such as friction losses, etc.

You can also calculate velocity purely from

(engine speed* gear ratios * final drive *) wheel circumfrence or
wheel rpm * circumfrence

This is assuming no slip (purely rolling condition). A more realistic slip ratio is 1.1 so for every 11 rotations of the wheel you go forward 10 wheel circumfrences.
I understand what you are trying to show with your graph, but it's pointless to make a distinction that HP and Torque are two separate things as they are so closely linked, and either can be used to show the same thing. It's good that you are trying to show that torque is the real driving 'force'.Eg Saying torque is important but power isn't is pointless, unless you make the caveat that you have set gear ratios.

If you don't have set gear ratios power is the only thing that matters, as that shows you what you can do in a given time. More power = more that can be done. When you nail the gear ratios down, it makes sense to talk in terms of torque only.
ps that's a pretty nice spreadsheet.

 

[Bob S]

In order to determine the maximum velocity of an automoble, you first need to determine the power loss due to drag and rolling forces, as pointed out above.

For automobiles, the drag power is the largest, and varies as speed-cubed:

P_drag = (1/2) ρAC_dv³

See http://en.wikipedia.org/wiki/Drag_(physics )

while rolling resistance power is

P_rolling =~0.01 mgv
where tire rolling resistance coefficient is ~ 0.01

Then match max engine power (torque x 2 pi RPM/60) to provide the necessary power. If, in an Excel run, the vehicle reaches maximum velocity before the engine reaches max power output, you will need a higher gear ratio.

Understanding the power loss due to drag, rolling reststance, etc., and knowing the engine brake (dynamometer) power, and using the acceleration rate vs velocity

P_acc = m a v

(mass acceleration velocity)

is sufficient to calculate elapsed times, final velocities, etc.

Bob S

 

[dehseth]

Thank you for your replies guys...

That spreadsheet I posted before does not belong to me, I found it on here. I've used torque, car mass, gear ratios and RPM to calculate vehicle's accerelation.
I actually want is max velocity that's all. Seems like this method is useful for me:

(engine speed* gear ratios * final drive *) wheel circumfrence or
wheel rpm * circumfrence

Let me ask you about this formula,

1. engine speed is RPM value right?

2. I have gear ratio and differantial ratio. And I multiply these two value to find a final ratio. In the formula above there's "final drive", what is final drive? In a regular car what value can I use?

3. here's how I found acc. Please correct if anything is wrong:
result torque = differantial ratio * chosen gear ratio * torque (at given RPM)
accerelation = result torque / mass of vehicle

So when calculating velocity, is it smt like this?:
result torque = differantial ratio * chosen gear ratio * torque (at given RPM)
velocity = result torque * 2pi * wheel radius

Thank you guys.

 

[xxChrisxx]

1. Yep engine speed is rpm.

2. Diff ratio is final drive. (its just a different way of saying it)

3. F = ma finds acceleration. Thrust at contact patch is F.
What you have found is wheel torque, to convert a torque a force you need a distance. T = Fd.

Thrust = wheel (resultant) torque * radius. (centre of wheel to ground.)

Velocity = Engine RPM * gear ratio * diff ratio * wheel circumfrence.

You don't need torque to find velocity.

 

[dehseth]

Velocity = Engine RPM * gear ratio * diff ratio * wheel circumfrence.

Ok I am not sure if I am doing it right.
I have shared a spreadsheet: http://spreadsheets.google.com/ccc?key=0ArPyqArltO-KdGxqX3l6WGJfTjUyTEwyUTZidkwtRHc&hl=en
This spread sheet is editable.
Spreadsheet includes RPM, torque, calculated gear ratios, HP, at the end velocity from formula but I guess I messed up at some point. I am using SI units (N, m etc..)


------------------------------------

And secondly I did a litle research about drag power. I found C_dA is approximately between 0.4-0.8 m² for regular cars. And air density is 1.2kg/m³ so final value is:
F_d = -0.3 * velocity² (velocity is in m/s)

Ok we may use these calculations also. I got torque, gear ratios, HP, RPM, wheel radius and F_d... I guess I need to subtract engine force on car (I mean the result force to make the car move forward) - F_d...

Well I kinda lost in here :)

Thank you...

 

[xxChrisxx]

Ok, sorry about this I should have made it more clear.

When referring to speed the ratio is a reduction ratio. So for example if you have a drive of 5:1 the engine is spinnign 5 times faster. However gears wrt to torque are multiplication ratios, 5:1 will increase torque 5 times. So if you've specified 5:1 as the gear ratio, you must use the inverse for speed reduction. ie 1/5.

So although I put both as multiply, I didn't make it clear that one was a reduction. I've edited the spreadsheet but can't seem to save it.

Edit also you've used, RPM directly which will give you mters traveled in a minute. You need to /60 to get seconds.

 

[dehseth]

Ok I guess you have edited spreadsheet. I see you change gear ratio as 1/gear ratio. And Divide RPM to 60 for converting m/min to m/sec.. So good till this point. But as you can see at table below km/h table, this car reach 105km/h at 1st gear which supposed to be a normal car, and at 5th gear I see 439km/h wow

Seems like I need to cut these values a litle bit. Do you have any proposition for that? What can I use to calculate air resistance, tire resistance etc...

 

[xxChrisxx]

I noticed that when I was editing it. Did you make these ratios up or use real data?

The diff seems a bit short, and the gears seem slightly too far apart.
I've edited them to give slightly more sensible answers.
your power outputs are calculated incorrectly. either do

Engine torque * engine RPM *(2pi/60) = Power
Wheel torque * Wheel RPM * 2pi/60 = Power.

The values should be the same.and the units need changing. You are calcualting power from Nm and radians/second. So your power output is in kW not horsepower

 

[dehseth]

I have a ford escort (2000) which is 90hp and I found gear ratios of ford: 3.35 1.99 1.33 1.00 0.68 (http://www.vibratesoftware.com/html_help/html/Ford/Ford_Transmissions_Main.htm#5%20Man )
I have changed these values on spreadsheet.

I might messed up with rpm-torque relationship cause I do not have real values. I am not sure these values belong to a standart car engine. And 1kW = 0.98630HP so it does not make too much difference when power is converted to HP. I still see e.g 1065155HP at cell M12 which does not make any sense..

And still there are absurd values at velocity table..

 

[xxChrisxx]

I have a ford escort (2000) which is 90hp and I found gear ratios of ford: 3.35 1.99 1.33 1.00 0.68 (http://www.vibratesoftware.com/html_help/html/Ford/Ford_Transmissions_Main.htm#5%20Man )
I have changed these values on spreadsheet.

I might messed up with rpm-torque relationship cause I do not have real values. I am not sure these values belong to a standart car engine. And 1kW = 0.98630HP so it does not make too much difference when power is converted to HP. I still see e.g 1065155HP at cell M12 which does not make any sense..

And still there are absurd values at velocity table..

I don't mean the relationship is messed up just that the way you have calcualted power is wrong. You are multiplying a torque figure at the wheel by an engine rpm. When you should be multiplying engine rpm by engine torque.

I've edited the first column of the power to calculate engine power output. That gives sensible figures. All other power outputs should be the same as this column.

Also the wheel looks a bit big for an escort (its 23 inches across). Plus you need to put a correct diffratio in, it'll probably be between 3.5 and 4.2.

 

[dehseth]

Ok yesterday thanks to Chris I finally got max velocity at certain gear and RPM...
Now I got accerelation and max velocity value.. I don't want to stop here, and I need more information and I think I can only get it from here somebody who knows about this topic.

I realized I need to adjust my accerelation values with actual speed. For example if you are doing 20kmph at first gear, and if you gear up to fourth gear car engine may stop or shake the car you know. So you won't get accerelation, you may even break something in transmission. Like you cannot start a car at fifth gear right? So you need velocity to use gears effectively. My accerelation values only depended on gear ratio, torque at given RPM, vehicle mass..

How can I involve current velocity to accerelation value?


Another issue is let's say you are traveling at 3rd gear and 4000RPM. When you shift up to 4th gear RPM value decreases to between 2000-2500.. How can I calculate smt like that?

 

[rcgldr]

Like you cannot start a car at fifth gear right?

You can, but you'd be slipping the clutch for a bit, and acceleration would be slow. On a Top Gear episode about the Corvette Z06 (you can find a few of these on youtube), Jeremy Clarkson claims to do a 0 to 160 mph run in 5th gear, but looking at the gauges the car was in 4th gear, which redlines at 175 mph at 7000 rpm, and Jeremy mentions the 175 mph speed in that segment, so my guess it was done in 4th gear, although the early scene shows him shifting into 5th gear. The Z06 reaches it's top speed of 198 mph in 5th gear at just over 6300 rpm, the rpm of it's peak power. The engine has adequate power at 1000 rpm to do this, but you'd have to slip the clutch until the car reached 32 mph for the engine to run at 1000 rpm without slipping the clutch.

The point here is that for maximum speed, the car needs to be geared so that maximum speed is reached at the rpm of peak power for an engine, not the engine's redline.

shift from 3rd to 4th gear at 4000 rpm, what is 4th gear rpm?

Just multiply 4000 by (4th gear ratio) / (3rd gear ratio).

 

[dehseth]

The point here is that for maximum speed, the car needs to be geared so that maximum speed is reached at the rpm of peak power for an engine, not the engine's redline.

My problem is I need to adjust accerelation value. If you start your car at 4th gear it won't accerelate as fast as 1st gear right? So how can I adjust my acc. values?

 

[rcgldr]

Acceleration values

Depends on how accurate you want this to be. The force at the rear tires = (engine torque) x (overall gearing) x (efficiency factor) / (tire radius). For efficiency factor .85 would be a good approximation. You could use a spread sheet to calculate acceleration versus speed (based on torque versus rpm) versus gear, assuming that you shift up at redline or when the force versus speed curve drops below the curve for the next gear.

 

[nucleus]

You have to determine two things. 1: Your power required which is the force available at the contact between the drive wheel tyres and road and is known as 'tractive effort'. The ability of the drive wheels to transmit this effort without slipping is known as 'traction'. Hence usable tractive effort never exceeds traction. The tractive effort relate to engine power as per formula in site below.

And 2: Your resistance or power required. Also formula for it is in site below.

In order to accelerate a vehicle, climb a hill, or pull a trailer, or a combination of them; your power available must exceed power required.

You can’t simply ignore resistance in the real world because drag varies as the square of the velocity and power by the cube. In other words, to double your speed you need to increase your power by a factor of eight!

The part about final drive is for some vehicles, such as tractors, that have high torque often have a planetary gear between differential and wheels. You can ignore it for cars or leave it as 1:1.

Chapter 31 of the following site has a lot of information:
http://www.the-crankshaft.info/2009/09/automobile-technology.html

Another book, which explains this, is “Principles of highway engineering and traffic analysis by Fred Mannering”, which is a book used to design highways. In chapter 2 of the book he gives detailed information of acceleration requirements for vehicles. I can’t find the book on the web but the following site contains parts of the book, starting on page 9:

http://transp.rpi.edu/~civl2030/classnotes/exam1_review.pdf

 

[xxChrisxx]

My problem is I need to adjust accerelation value. If you start your car at 4th gear it won't accerelate as fast as 1st gear right? So how can I adjust my acc. values?

You should have an adjusted wheel torque value (which you do). The 4th gear value will be much lower than the 1st gear value. You don't need to adjust it from that sense.

However so far no losses have been included, they would reduce the accceleration.

 

[dehseth]

@Jeff Reid I'm kinda rookie on these things. I am a software engineer, and I do not know much about cars. I want to simulate a vehicle using engine HP, gear ratios, and torque. Actually I kinda don't get what you mean, sorry.

@nucleus That crankshaft website is wow, but there's too much info in it. I want basic simulation. As I understood you want me to calculate power and use that values. It might be a good idea to do that but I need more help.

1. First of all I would like to ask you both should I use SI metrics (Nm, m etc) or English/American metrics (lb, feet, etc). Beacuse at the end I want to obtain instant accerelation at certain RPM and gear, and instant velocity at certain RPM and gear. It is easy to conver mph to kmph. What do you think on that?

2. After deciding units, what I have is: gear ratios, RPM, torque. I can calculate hp (kW) from here. And I can calculate the torque at wheels. And the drag power against car at certain velocity.

3. After calculating acc and velocity, in near future I would like to have engine brake it user is not touching anything the car slows down and it also depends on gear and velocity. And hitting brake will slow down car, I think this won't be a problem. One more thing if the car is moving uphill/downhill there's gravity factor which won't be a problem if I can calculate over all force on car right

Can you make comments on these 3 topics? I probably need our help when I start to calculate smt. It would be best if I can open a editable spreadsheet so anybody can make comments. Thank you guys.

 

[xxChrisxx]

I assume you have having issues with thinks like clutch slip?

If you try to start your car in 4th from idle. It probably won't transmit enough power to turn the wheel (or possibly spin it because it will be rotating too quickly) and as a result no motion at the wheel means the engine must also stop, so you stall.

What slipping the clutch does is allows the engine to remain above idle revs, but transmit less power and rpm along the transmission. It's when you bring the clutch up through the bite point slowly. It basically acts as a constantly variable gear ratio, the higher you lift it, the more powre it transmits.

The problem with this is it put a lot of wear and starin on te clutch.

You don't been to worry about altering acceleration for different gears, because we've already don't that by calcualting wheel torque in each gear.1. Use whatever units you feel most comfortable with it's easy to convert. Normally I stick with 1 typre for all calcualtions then convert the end results (stops roundning and conversion errors).

2. yep Use dragpower to work out speed, but you can also work out drag force, which will alter acceleration. (in reality yiu can do it either way but I like to use force for acceleration).

3. I don't get this question.

 

[dehseth]

Hey Chris,

I just posted a comment before you did. Can you make comments on that? What would you suggest? Should I start over, this time calculating forces on car and let the calculation determine max speed at certain gear and RPM?

 

[xxChrisxx]

Hey Chris,

I just posted a comment before you did. Can you make comments on that? What would you suggest? Should I start over, this time calculating forces on car and let the calculation determine max speed at certain gear and RPM?

I've just edited the post. Don't restart, what you've got now is fine.

You just need to add force and acceleration cells. There is no point doing it the other way, as if the model is correct you'll come up with the same answer.

 

[dehseth]

It is not easy to find SI unit examples and explanations on internet maybe I should stick with English units all the time.

I have added accerelation at the bottom of sheet (http://spreadsheets.google.com/ccc?key=0ArPyqArltO-KdGxqX3l6WGJfTjUyTEwyUTZidkwtRHc&hl=en)
Sheet is editable. I divided output torque to car mass value to find accerelation, is it correct? I believe this accerelation value is in m/s², I am not sure about that.

And I am a bit confused actually:
F = m . a So I got a and m if I multiply car mass with acc I found F force on car. Which is torque value in my calculation.

But tork = F . r F force, r radius of wheel.. So smt is wrong...


About my previous 3rd question: If the car is moving uphill with slope of 30 degrees the car has a negative force since there's gravity. How should I include those later.. I guess we should go step by step to we don't get confused...

 

[xxChrisxx]

It is not easy to find SI unit examples and explanations on internet maybe I should stick with English units all the time.

I have added accerelation at the bottom of sheet (http://spreadsheets.google.com/ccc?key=0ArPyqArltO-KdGxqX3l6WGJfTjUyTEwyUTZidkwtRHc&hl=en)
Sheet is editable. I divided output torque to car mass value to find accerelation, is it correct? I believe this accerelation value is in m/s², I am not sure about that.

And I am a bit confused actually:
F = m . a So I got a and m if I multiply car mass with acc I found F force on car. Which is torque value in my calculation.

But tork = F . r F force, r radius of wheel.. So smt is wrong...About my previous 3rd question: If the car is moving uphill with slope of 30 degrees the car has a negative force since there's gravity. How should I include those later.. I guess we should go step by step to we don't get confused...

You need to convert torque to force. T = Fd
So you take your torque value and divide by rolling radius. This gives the force at the contact patch.

Torque / mass gives units of = m^2/s^2

Also car mass is in kg. 1100kg is the mass of the car.
For the third question, we can deal with that later. Goping up a hill is a set force pushign backwards determined by mass gravity and slope angle. Thats really easy to do.

F = mg sin (angle)

 

[dehseth]

Ok let's see

T = F.d so F = T/d

and F = ma so T/d = ma

therefore a = T/(d . m)

I guess 1100kg is weight of a car so I should divide it by 9.8 gravity, right?

 

[xxChrisxx]

Ok let's see

T = F.d so F = T/d

and F = ma so T/d = ma

therefore a = T/(d . m)

I guess 1100kg is weight of a car so I should divide it by 9.8 gravity, right?

you just use 1100.
The acutal weight of the car is 1100*9.8.

This is one of the things where common usage of the word weight is not strictly correct in a scientific sense.

 

[dehseth]

Ok I have edited accerelation table in spreadsheet.
Now I got m/s². Should I convert it to km/h² to use it? This is a lil bit confusing to me actually. Cause I guess I need to multiply each value with (36*360) so I get km/h²?

 

[xxChrisxx]

Ok I have edited accerelation table in spreadsheet.
Now I got m/s². Should I convert it to km/h² to use it? This is a lil bit confusing to me actually. Cause I guess I need to multiply each value with (36*360) so I get km/h²?

Just leave it as m/s^2. It doesn't really matter as the trends will be the same in either case.

 

[dehseth]

So I can use m/s² when increasing speed to top speed. Do you think those acc values on sheet are correct?

[STRIKE]Next question is when using manual transmission, if user shiftup's too early is the car still accerelates as calculated on the acc table values?[/STRIKE]

-- Well seems like I can use table.. Car does not accerelate immediately...

Next question is if there's wind how should I consider that? I guess I can calculate wind's drag power over car using P_d formula.. And I can change that Power to Force and therefore I can calculate change in accerelation right?

 

[rcgldr]

What slipping the clutch does is allows the engine to remain above idle revs, but transmit less power and rpm along the transmission.

The main power loss that occurs when slipping a clutch is the power lost due to heat generated by the friction. Unlike a CVT (continuously variable transmission), a manual clutch does not increase the torque (other than momentum effect if suddenly engaged). A fluid clutch on some automatics has some torque multiplier efect because the driving vanes are located outside the driven vanes (larger radius for the driving vanes).

When launching from a standing start, the clutch allows the engine to run at a higher rpm, higher torque output, and the torque applied to the drivetrain after losses due to clutch slipping is larger than the torque would be at a lower rpm, lower torque output from the engine with no clutch slipping losses.

For many street cars though, the slipping coefficient of friction of the clutch is relatively low, and it's faster to launch by dropping the clutch and spinning the tires instead because the tires dynamic friction is better than the clutches dynamic friction after taking gearing into account.

I've done a similar thing for a motorcycle using a spread sheet but I knew the top speed in advance from an actual test done in a magazine. Acceleration at top speed is zero, so the drag force is equal and opposite to the tire force, and I made the simplified assumption that drag force was related to speed².

drag force = (tire force at top speed) x ( (current speed) / (top speed) )².

tire force = (torque at rpm) x (overall gear ratio) x (efficiency factor) / (effective tire radius)

current speed (in units per second) = (rpm) (2 x pi x effective tire radius) / (60 x overall gear ratio)

total force = (tire force) - (drag force)

dividing force / mass will give you acceleration values. I would use .85 to .87 as an efficiency factor for a car. You'll then need to use some form of numerical integration to estimate increase in speed versus time and distance versus time.

 

[dehseth]

Thanks Jeff. I think I can come up smt with all of these information. I will ask you more guys if I get stuck again..