Defining 'Grunt' - Interested?
Discussion
As some of you probably know my background is in engineering and I have a reasonable amount of experience of performance modelling of cars. I've noticed a few people talking about 'grunt', 'torque', 'engine flexibility', etc. and in fact arguing over whether a Honda S2000 has a flexible engine or not, i.e. is it too 'cammy'? I think I have a good theory on how the true 'grunt' of a car can be measured but it would take a while to detail and I'm wondering if anyone would be interested in reading it, otherwise I won't bother? So... let me know please!
roadsweeper.
roadsweeper.
) 
Easy!
You're driving along normally (a loose definition, I know!), and you put yer foot down. Then you'll know.
Grunt = strong acceleration in any gear and at any engine speed.
Of course, having a Seicento Sporting, I'm more familiar with "hysterical screaming and cursing when approaching a hill".
You're driving along normally (a loose definition, I know!), and you put yer foot down. Then you'll know.
Grunt = strong acceleration in any gear and at any engine speed.
Of course, having a Seicento Sporting, I'm more familiar with "hysterical screaming and cursing when approaching a hill".
Here goes...
OK, what we're trying to find is a car that can accelerate at some rate defined as 'reasonable' over a engine speed range definined as 'wide'. Acceleration is governed by the equation
(1) F = m.a
Where F is force (Newtons, N), m is mass (kilogrammes, kg) and a is acceleration (metres per second per second, m/s/s).
We rearrange the formula to give a instead of F
(2) a = F / m
So ultimately, if we know the mass of the vehicle, m (reasonable assumption) then if we can find the motive force F (force generated at the wheel) generated by the engine throughout the rev range in each gear then we can find an acceleration curve for the vehicle at engine speed, in any gear - i.e. we can measure the engine's 'flexibility'.
To find the motive force we need to do the following:
Using a dyno graph of the engine, the gear ratios and the final drive ratio we take the engine torque at every, say, 250rpm and multiply it by the gear ratio and the final drive ratio, that gives us torque at the wheels (I've ignored losses in the transmission as this is relatively difficult to measure and we can assume there's not much in it when comparing like for like in terms of drivetrain, e.g. RWD vs RWD, etc.).
(3) T(wheel) = T(engine) x R(gear) x R(final drive)
Torque and force are related by the equation
(4) T = F.r
Where T is torque (Newton-metres, Nm), F is motive force (Newtons, N) and r is the moment arm (metres, m), which in this case is the distance from the centre of the wheel to the outside of the tyre.
We rearrange the formula to give F instead of T:
(5) F = T / r
Substituting equation 3 into equation 5 gives:
(6) F = [ T(engine) x R(gear) x R(final drive) ] / r
Now substituting equations 3 and 5 into equation 2 gives
(7) a = [ T(engine) x R(gear) x R(final drive) ] / m.r
If we apply equation 7 to a torque curve (easy using a spreadsheet) then we can see how well a car would actually accelerate at any given engine speed in any gear, all other things being equal (aerodynamic resistance, drivetrain friction, etc.). It takes account of the actual mass of the vehicle and it's gearing, which can make an engine 'grunty' in one car and not in another (hence the Lotus Elise with it's 1.8 engine that someone described as grunty). To me this is exactly what defines 'grunt' (I think!). In reality there would clearly be some problems with stalling at low revs but I don't think this would show in the data.
So, if anyone has a torque curve for their car and can get the gear ratios plus final drive for said car (will be in the manual) we should be able to say whether it is grunty or not by comparing it to, say, a Chimaera 400, (Griffith 500 might be a bit of a mighty comparison!
) and seeing if it can match it's acceleration curve. (Also need the wheel diameter including the tyre too). Anyone volunteer that info?
Phew! Bit much for a Friday afternoon but I'm bored with nothing to do and needed to get this out of my system. (Sad b@st@rd that I clearly am).
roadsweeper.
PS: If I've made any mistakes or the formula can be improved with something that is easy to measure then please let me know.
OK, what we're trying to find is a car that can accelerate at some rate defined as 'reasonable' over a engine speed range definined as 'wide'. Acceleration is governed by the equation
(1) F = m.a
Where F is force (Newtons, N), m is mass (kilogrammes, kg) and a is acceleration (metres per second per second, m/s/s).
We rearrange the formula to give a instead of F
(2) a = F / m
So ultimately, if we know the mass of the vehicle, m (reasonable assumption) then if we can find the motive force F (force generated at the wheel) generated by the engine throughout the rev range in each gear then we can find an acceleration curve for the vehicle at engine speed, in any gear - i.e. we can measure the engine's 'flexibility'.
To find the motive force we need to do the following:
Using a dyno graph of the engine, the gear ratios and the final drive ratio we take the engine torque at every, say, 250rpm and multiply it by the gear ratio and the final drive ratio, that gives us torque at the wheels (I've ignored losses in the transmission as this is relatively difficult to measure and we can assume there's not much in it when comparing like for like in terms of drivetrain, e.g. RWD vs RWD, etc.).
(3) T(wheel) = T(engine) x R(gear) x R(final drive)
Torque and force are related by the equation
(4) T = F.r
Where T is torque (Newton-metres, Nm), F is motive force (Newtons, N) and r is the moment arm (metres, m), which in this case is the distance from the centre of the wheel to the outside of the tyre.
We rearrange the formula to give F instead of T:
(5) F = T / r
Substituting equation 3 into equation 5 gives:
(6) F = [ T(engine) x R(gear) x R(final drive) ] / r
Now substituting equations 3 and 5 into equation 2 gives
(7) a = [ T(engine) x R(gear) x R(final drive) ] / m.r
If we apply equation 7 to a torque curve (easy using a spreadsheet) then we can see how well a car would actually accelerate at any given engine speed in any gear, all other things being equal (aerodynamic resistance, drivetrain friction, etc.). It takes account of the actual mass of the vehicle and it's gearing, which can make an engine 'grunty' in one car and not in another (hence the Lotus Elise with it's 1.8 engine that someone described as grunty). To me this is exactly what defines 'grunt' (I think!). In reality there would clearly be some problems with stalling at low revs but I don't think this would show in the data.
So, if anyone has a torque curve for their car and can get the gear ratios plus final drive for said car (will be in the manual) we should be able to say whether it is grunty or not by comparing it to, say, a Chimaera 400, (Griffith 500 might be a bit of a mighty comparison!
) and seeing if it can match it's acceleration curve. (Also need the wheel diameter including the tyre too). Anyone volunteer that info? Phew! Bit much for a Friday afternoon but I'm bored with nothing to do and needed to get this out of my system. (Sad b@st@rd that I clearly am).
roadsweeper.
PS: If I've made any mistakes or the formula can be improved with something that is easy to measure then please let me know.
Before anyone lays in to me, you (literally) asked for it so I won't accept any jibes from people who told me to go ahead. Unless you were all joking of course, in which case I'll feel really stupid! 
Actually, thinking about it, I don't know why I bothered with the above excuses - I've got my Nomex suit on so flame away!
Actually, thinking about it, I don't know why I bothered with the above excuses - I've got my Nomex suit on so flame away!
quote:I can see where you're coming from, although some might argue that a Range-rover has a lot of grunt, but they don't exactly accelerate very fast (because it's your 2.5 tonne behemoth
craigalsop: Partly right, but ignores mass, so you could have a 2.5 tonne behemoth that blunts it's fantastic engine. (Think Arnie Schwarzenegger pushing Vanessa Feltz
And no, I don't think either of those names are spelt correctly either!
roadsweeper.
) cheers,
Craig
Well, I'd say the simple way is if you don't have to change gear too much to go fast. I have turboed car so need to be in the right gear all the time to get the most out of it i.e. not very grunty.
Get in a Griff 500 or a Cerbie and you can be a crap driver and still drive it fast. Sure some of you can testify that I'm right here
Get in a Griff 500 or a Cerbie and you can be a crap driver and still drive it fast. Sure some of you can testify that I'm right here
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