Theoretical Maximum Speed Calculator (v2016)

[Bobby Dazzler]

In the past I have calculated the theoretical maximum speed for members. For many it's just a bit of fun, but it has also been used to help inform those who are taking part in competition or modifying their cars. It's also been used to challenge the claims of manufacturers and press reports.

The calculation is based upon sound and accepted engineering theory, and inevitably simplifications are made for the ease of calculation. For example the effects of gearing and tyre slip are not factored in to the calculation. However the calculated theoretical top speed is usually remarkably accurate when compared to benchmark data.

I'm very happy to calculate the theoretical maximum speed of your vehicle or any other vehicle you have an interest in providing that the following conditions are met:

• You provide the information (see below), I don't have time to go Googling for it!
• You understand that it's calculated and theoretical. The rest of us do!
• You don't get shirty, and challenge it based upon it not taking 'X' into account
• You don't mind if it takes me a while to post the resul, although I'll usually post pretty quickly
• You don't mind me storing the information you provide for future reference

In order to calculate the theoretical maximum speed of your car I need the following information, note units of measure are shown in brackets:

Member's name
Model
Transmission losses (%)
Power @ flywheel (BHP)
Vehicle track (m) - see note below *
Vehicle height (m)
Mass [weight] (kg)
Drag coefficient

* Front and rear track are typically different - lease provide the widest track.

Please post the required information in EXACTLY this sequence, quoting the most credible source available, and If required convert to the required units of measure BEFORE posting. This enables me to copy/paste your data into the calculation without interpretation. For example:

Mrs Dazzler
ML63 AMG Performance Pack
0.18
630
1.665
1.86
2376
0.38

I'll then quote the post in which you provide this information, and of course I will add the calculated theoretical top speed.

So feel free to post if you'd like to calculate the theoretical top speed for your car!

 

[Bobby Dazzler]

So in case you're wondering what the sound and accepted engineering theory is, here's a quick summary:

The top speed of a vehicle is influenced by the following factors:

• coefficient of rolling resistance [0.025 for preumatic tyre on tarmac]
• vehicle mass (weight) (kg)
• air density [at 200m altitude: 1.202 kg/(m*m*m)]
• drag coefficient (also commonly referred to as Cd)
• maximum vehicle cross section (m*m)
• headwind speed
• gradient angle (degrees)

Please do bear in mind that because I don't have greek alphabet charachters and subscript fonts I've had to be a little creative with the symbols I've used, but I've explained them all at each point, so it should be fairly clear as you work through.

Maximum speed is attained when the power output of the engine is equal to the running-resistance power (Pw):

Pw = Fw * V

where,
Pw is motive power (kW)
Fw is running resistance (N)
V is vehicle speed (km/h)

The running resistance is calculated as (Fw):

Fw = Fro + Fl +Fst

where,
Fw is running resistance (N)
Fro is rolling resistance (N)
Fl is aerodynamic drag (N)
Fst is climbing resitance (N)

The rolling resistance (Fro) is the product of deformation processes which occur at the contact patch between the tyre and the road surface:

Fro = F * M * G

where,
Fro is rolling resistance (N)
F is coefficient of rolling resistance [0.025 for preumatic tyre on tarmac]
M is vehicle mass (weight) (kg)
G is gravitational acceleration [9.81m/(s*s)]

Aerodynamic drag (Fl) is calculated as:

Fl = 0.5 * Ro * Cw * A * (V + Vo) * (V + Vo)

where,
Fl is aerodynamic drag (N)
Ro is air density [at 200m altitude: 1.202 kg/(m*m*m)]
Cw is drag coefficient (also commonly referred to as Cd)
A is maximum vehicle cross section (m*m)
V is vehicle speed (km/h)
Vo is headwind speed (km/h)

The climbing resistance (Fst), or downgrade force (Fst), are calculated as:

Fst = M * G * sin(Alpha)

where,
Fst = Fst is climbing resitance (N)
M is vehicle mass (weight) (kg)
G is gravitational acceleration [9.81m/(s*s)]
Alpha is gradient angle (degrees)

 

[Bobby Dazzler]

So Mrs D will get the ball rolling:

Mrs Dazzler
ML63 AMG Performance Pack
0.18
630
1.665
1.86
2376
0.38

 

[Bobby Dazzler]

So Mrs D will get the ball rolling:

Mrs Dazzler
ML63 AMG Performance Pack
0.18
630
1.665
1.86
2376
0.38

Theoretical VMax 181 mph

 

[Bobby Dazzler]

I hope Dave doesn't mind me using his car as an example.

daveenty
E63 AMG (W212)
860
1.625
1.471
1840
0.36

Theoretical VMax 226 mph

Source for power output

 

[Bobby Dazzler]

I hope Lee doesn't mind me using his car as an example.

Lee C63
C63 AMG (W204)
725
1.659
1.433
1730
0.32

Theoretical VMax 221 mph

Source for power output

 

[Deleted member 113659]

Are you ok Rob?

 

[Bobby Dazzler]

Are you ok Rob?

As OK as I'll ever be

 

[daveenty]

I hope Dave doesn't mind me using his car as an example.

Not in the slightest, Cheers Rob. It will be going to TV next year hopefully so we can get a vague idea what it is capable of. This was the main reason for doing it anyway, and Bruno's already pestering me about it.

I hope Lee doesn't mind me using his car as an example.

Sod him, he's away at this moment in time anyway, but I'm sure he'll be happy.

 

[Peter103]

A few years ago I owned a BMW 335 d, auto car de limited one and actually drove it and recorded 186 MPH. I'm wondering what my E350 9g would come in at and hoping another member that has one, ,provides you with the required information, Of course.if your not too busy...............Fascinating thread!

 

[C43AMG]

I'm not sure where to find the transmission loss ?

 

[daveenty]

I'm not sure where to find the transmission loss ?

It's always a problem Peter, and I don't have a lot of confidence in the figures which most people tend to assume and quote. Our cousins across the pond just tend to quote rear wheel figures, which is what they're actually seeing on the print out and, at least in my mind, is a lot more accurate. It would make life a lot easier if everyone did this, but the vehicle manufacturers are as much to blame as anyone for the engine figures which are quoted.

A general rule, and used by a lot of people is as follows: -

• Front Wheel Drive = Add 15%
• Rear Wheel Drive = Add 18%
• Four Wheel Drive = Add 22%

However, once the horsepower starts to rise it tends to get a bit fuzzy, as some of the alleged loss through the transmission would be generating enough heat to run a small town. Also these figures tend to vary dependant on the transmission type. A manual would theoretically lose less than an auto for example. A multi clutch less that a torque converter and so on.



To me, the only way of getting an accurate reading would be to take the engine out and run it on an engine dyno, but this is obviously not going to happen, so I'll just stick with the 18% and follow the herd.

 

[AMGeed]

I hope Dave doesn't mind me using his car as an example.

daveenty
E63 AMG (W212)
860
1.625
1.471
1840
0.36

Theoretical VMax 226 mph

Source for power output

When you think about it, that is just an incredible theoretical speed from a 4 door 5 seat family saloon. I would be highly impressed at anything 200+ to be fair.

Lee's shed can shift a bit too

 

[daveenty]

When you think about it, that is just an incredible theoretical speed from a 4 door 5 seat family saloon. I would be highly impressed at anything 200+ to be fair.

Yeah, not bad for an old Taxi. Bear in mind I have done a bit to it though Roger...

Lee's shed can shift a bit too

Lee's car makes me happy, and I still blame him for what I've done with mine. Let's face it, he was the first to do any serious mods really.

 

[C43AMG]

I'm bound to have got this completely wrong !!

C43AMG
W216 6.3 biturbo
18%
544 BHP
1,419 Height
2,585 Kg
1,601 Track
.29 Drag

 

[Iceviolet]

That's one heavy c class!

 

[Iceviolet]

That's one heavy c class!

My bad, it's cl, I just saw your user name!

 

[C43AMG]

That's one heavy c class!

2.8 tons in old money and 2.3 tons Kerb weight

 

[John]

2.8 tons in old money and 2.3 tons Kerb weight

You sure it is that heavy (not sure is 2.5 as per your post #15 or 2.3 above)?

Mine is 2070kg... albeit a 4.7 V8.

Just wondering if you've clocked the revenue weight instead...

 

[m2287]

I'm bound to have got this completely wrong !!

C43AMG
W216 6.3 biturbo
18%
544 BHP
1,419 Height
2,585 Kg
1,601 Track
.29 Drag

Have you just let slip what your new motor is