4wd vs 2wd (Jeremy Clarkson's proof)

  • Thread starter aeb2335
  • Start date
  • Tags
    Proof
In summary, when comparing a 2wd and 4wd car in a drag race, it is important to consider factors such as weight transfer, parasitic drag, and power distribution. While 4wd may have an advantage in initial acceleration due to increased traction, the additional weight and power losses in the drive train may ultimately give the 2wd car the edge in achieving the highest velocity in a straight line over a set distance. However, drag races are not always a reliable way to compare cars, as there are many other factors at play and a poor driver can greatly affect the outcome.
  • #1
aeb2335
26
0
This question of 2wd vs 4wd in a drag race has bugged me for a bit and I was wondering if my conclusion makes scene. Most of the time that I can remember a 2wd will win over a similar 4wd car and I wanted some mathematical proof on why that is. I am not entirely sure where to begin this one...

Given:
(gross assumptions)
Both cars have the same mass, same moment of inertia for all four wheels, same wheel radius, both cars produce the same amount of power and torque. Both undergo rolling without slipping (just for simplicity) and assume that the coefficients of friction and rolling resistance is the same for all four wheels and between cars.

Find:
In a drag race over a set distance what car would achieve the highest velocity the fastest

Analysis: well I am kind of lost right now...but in essence my thinking is this...
sumtorques=Ia
2wd: T/2=Ia
4wd: T/4=Ia

So a 2wd car's wheels (and thus acceleration as atan*r) at a given power will be 2x that of a 4wd car...i feel like something is missing i made a free body diagram etc. but because the mu kenetic is the same on all four wheels and between cars the total loss for both cars is the same...help?
 
Physics news on Phys.org
  • #2
For most street cars 4wd has an advantage at the launch because there isn't enough acceleration or high enough center of mass to transfer almost all of the weight onto the rear tires so there's some grip to be utilized at the front. In a real world situation, this will be offset somewhat by the increased mass and power losses in the more complicated drive train.

For high end dragsters (and motorcycles), almost all or all (wheelie) of the weight is transferred to the rear tires so 4wd doesn't offer any advantage.
 
  • #3
A modern 4wd will give you better acceleration in a straight line than an FR 2wd, as they aren't that much heavier these days and inital acceleration (where drags are won and lost between similar powered cars) is traction limited. Having 4 wheels driving gives a bigger tyre footprint to put more power down. This is expecially true if there is some computer trickery that feeds the power to the wheels with the most traction.

Porsches are notoriously good off the line with 2WD becuase the engine is sat over the back axle allowing higher traction. If we assumed a tyre that had infinite tractive capabilities, then a RWD car will probably beat the 4WD as it would be that little bit lighter.

Although to be honest drag races are awful ways of comparing cars. Crap driver = craptimes.
 
  • #4
Given:
(gross assumptions)
Both cars have the same mass, same moment of inertia for all four wheels, same wheel radius, both cars produce the same amount of power and torque. Both undergo rolling without slipping (just for simplicity) and assume that the coefficients of friction and rolling resistance is the same for all four wheels and between cars.

There are many problems with this static analysis..
PARASITIC DRAG
1. both cars produce the same amount of power and torque means the 4wd car will LOSE big time.
Drive train parasitic drag will suck anywhere form 100 to 150 HP...just compare the Dyno HP of an engine to that of a chassis dyno after that engine is installed in the vehicle. The 2wd car will be able to deliver more useable HP to the pavement.

WEIGHT TRANSFER
2. Both cars have the same mass, This means the REAR WHEEL DRIVE ONLY car has a lot more sprung weight that can be transferred to the rear wheels to make more traction. The 4wd car has two massive differentials , and you are literally taking weight off the front drive wheels and dumping it on the rear drive wheels under acceleration. Just not as effectively as the 2wd.

this is why the drag race boys still use 2 wheel rear drive set ups in the unlimited classes where anything goes. TV Tommy Ivo and Mickey Thompson tried all wheel drive systems in the early 1960's..Hurst Hairy Oldsmobile used the front wheel drive Toranado and dumped another engine/ drive train in the trunk for a ground shaking all wheel drive drag car...
 
  • #5
With all of that said: Is it possible for the front wheels on an FWD to lift completely off the ground under acceleration? I know they won't stay in the air for long.
 
  • #6
not likely
 
  • #7
aeb2335 said:
Analysis: well I am kind of lost right now...but in essence my thinking is this...
sumtorques=Ia
2wd: T/2=Ia
4wd: T/4=Ia

So a 2wd car's wheels (and thus acceleration as atan*r) at a given power will be 2x that of a 4wd car...i feel like something is missing i made a free body diagram etc. but because the mu kenetic is the same on all four wheels and between cars the total loss for both cars is the same...help?

Not sure what the logic here is, but no a 2wd car shouldn't accelerate 2x faster than a 4wd, nor will the wheels because they're all connected to each other as well as to the car itself. In order for one thing to accelerate, EVERYTHING has to accelerate.

However, yes you're running more power through each wheel in a 2wd car than through a 4wd car, so if you were to lift the car off the ground...then yes 2 wheels would be easier to accelerate than 4 (although it won't be 2x faster due to all the other masses that need to be accelerated such as engine, flywheel, transmission, etc).
 
  • #8
Lsos said:
Not sure what the logic here is, but no a 2wd car shouldn't accelerate 2x faster than a 4wd, nor will the wheels because they're all connected to each other as well as to the car itself. In order for one thing to accelerate, EVERYTHING has to accelerate.

However, yes you're running more power through each wheel in a 2wd car than through a 4wd car, so if you were to lift the car off the ground...then yes 2 wheels would be easier to accelerate than 4 (although it won't be 2x faster due to all the other masses that need to be accelerated such as engine, flywheel, transmission, etc).

Logic: if you know the angular acceleration of the wheels which is the resultant of a torque and if you know the radius of the wheel then that acceleration can easily be translated into the translation of the total body At= alpha*r. On the everything accelerating front if the acceleration at the wheels is less the entire body's acceleration will be less relative to the other car as the masses are the same.

The point of the problem in this particular frame is to figure out what is a fundamentally better platform. I do understand that the "real world" must enter into it and I completely agree that it will not really accelerate 2x as fast. However, the problem with that becomes the fact that you must know/be able to account for all mechanical losses of the entire drive train (which can vary from specific car to car) and then you have to think about drag and the list goes on. But again the point is to try and figure out what the best starting off point would be from an engineering perspective and why. Obviously straight line speed is not the most representative metric of a cars performance but it is the simplest case I could think of to compare the two right off the bat. I do plan on looking at a similar question with both cars at an entry speed at a corner to determine who slips first.

I did like that insight about mass transfer (i don't know much about that so that will be this evenings wiki quest)

On an unrelated note I really appreciate the responses
 
  • #9
I think if you can find a textbook on vehicle dynamics or one with vehicle dynamics in it you should find a more appropriate way to calculate this. When I din Mechanics 3 we were taught how to convert the cars to an equivalent moment of inertia. This enabled us to determine the "ideal case acceleration" of the car. there is also a way to convert the wheel moment of inertia to an equivalent mass but that also requires you to convert the torque on the wheel to an equivalent force. They should both give you similar acceleration results.
 
  • #10
Looking at angular accelerations is the wrong way to go about it, especially assuming infinite grip.

A better starting point would be assume:
A maximum amount of grip.
Angular acceleration of the wheels is small compared to the acceleration of the car.
Assume no weight transfer.
Assume no losses.


Acceleration is limited by:
1. Traction limited.
2. Power limited.


1. Traction limited.
With high power cars during the inital phase of acceleration, there is far too much power for the tyres to handle, and they spin up.
You can cure this by:
removing power input (modulating throttle or traction control)
Increasing grip by using better tyres, or using more driving wheels.

4WD vechicles accelerate much much better than 2WD in low grip conditions. A visualisation of this is cars on gravel (same situation as initial acceleration more power than grip) where we know for a fact that 4WD is king.


2. Power Limited.
After the tyres have stopped spinning up, you are power limited. Acceleration is limited becuase the tyres are capable of more power than the engine is delivering. The ways to solve this are increase power or decrease losses.

In this situation weight will be the killer due to Newtons 2nd law. 4WD is heavier.
Also dumb 4WD systems, will send equal power to all wheels. When weight transfers to the rear, there will be more rear grip.

The answer to this is torque sensing/active central diffs, in full traction conditions send all the power to the rear.



Conclusion:

The success or failure of a straight line drag race of a RWD or 4WD car will depend on the relative amounts of time spend in the traction and power limited conditions.

The higher the proportion of time spent in the traction limited condition will favour the 4WD. The higher the propoertion of time spent in the power limited condition will favour the 2WD.

EDIT: Disclaimer.
This is all idealised. In reality you tend to find that AWD vechicles have too much grip on the start and that bogs the engine down, or you destroy the clutch/driveshafts.

It takes cars with lots of computers and smart TC systems to sort this out. The result is this Which launches like a scalded cat.
 
Last edited:
  • #11
Why would you be worried about being traction limited if you have infinite grip?
 
  • #12
yster said:
Why would you be worried about being traction limited if you have infinite grip?

Becuase assuming infinite grip isn't even remotely realistic. I suppose I wasn't clear before.

Looking at angular accelerations is the wrong way to go about it, especially assuming infinite grip.

For inital purposes (with no real tyre data) a nominal maximum value for traction should be assumed. NOT infinite grip.
 
Last edited:
  • #13
as usual xxxchrisxx does it again...nice one amigo! does it have air conditioning?
 
  • #14
Did you realize that the OP stated that both cars will "experience rolling without slipping"
The whole point of this is to try and give a theoretical solution i.e. if everything was perfect
 
  • #15
yster said:
Did you realize that the OP stated that both cars will "experience rolling without slipping"
The whole point of this is to try and give a theoretical solution i.e. if everything was perfect

Assume a spherical cow?

Engineering is about making correct assumptions, simplifying but not destroying reality.
Creating a scenario that doesn't reflect reality and then applying conclusions to reality, is meaningless.
 
  • #16
Isn't that exactly what we are taught at school, university, college etc. The more you progress the more you realize all the stuff you have been leaving out of your calculations. The point is to help you grasp the concept in its simplest form to make it easier for you to apply it in reality.
 
  • #17
yster said:
Isn't that exactly what we are taught at school, university, college etc. The more you progress the more you realize all the stuff you have been leaving out of your calculations. The point is to help you grasp the concept in its simplest form to make it easier for you to apply it in reality.

You should be taught not to make assumptions blindly. The idea is to judge what you can and can't leave out.

Assuming infinite grip for a car on a drag race, is a very bad assumption becuase almost all cars can break traction in first gear, leaving it out would mean a dreadful model that gives outputs bad enough that you can come to incorrect conclusions.


The spherical cow in a vacuum example, is a satirical joke. Becuase it's obvious the conclusions drawn from it are so oversimplified they are useless.
 
  • #18
4wd advantage is lost once the car's power level causes the front tires to unload to the point of having near zero traction.

Our twin turbo ford GT out accelerates an awd lamborghini gallardo all the way up to 253mph...soon to be 270
 
  • #19
Wow I leave to go into the wilderness with no internet and this thread is still going

Ok so after some light reading and thinking I have the following to say

Firstly as I (think) I stated before this is a highly theoretical what if scenario; as engineers or physicists we must be subject to the "real world" but in order to understand the imperfect we must eliminate the noise so that we can build a clear understanding from the ground up and as a result we end up with a spherical cow (thought: is that just an RIT thing?).

Now on to the good stuff

Earlier someone mentioned creating equivalent moments to solve this problem that was almost the correct idea frame terminology according Vehicle Dynamics Theory and Application by Reza N Jazar

The basic method of describing a car's 4wd RWD FWD characteristics is to treat it as a dynamic rigid body

Firstly we must calculate the car's centre of mass which will then summing moments about COM will yield the normal force at all the wheels.

There will be two components to this solution the static component (y,z) and dynamic component (x)

We must then assert that Fx= ma

Through some substitution magic it works out that the static component Y (based on COM) at the wheels governs grip and thus acceleration

Now that i am getting lazy and tired i will refer you to the book for these assertions but it further works out that if you get a perfectly balanced car with unlimited power 4wd is best...BUT

We must always account for the added weight of components and losses from them...and because power will never be unlimited that's just dumb

My conclusion RWD in a drag race will win on the following basis its simpler few transmission losses, lighter and as there WILL be weight shift towards the rear increasing the possible grip at those wheels RWD wins...and it would make sense to put an engine at the rear in that case...
 
  • #20
aeb2335 said:
This question of 2wd vs 4wd in a drag race has bugged me for a bit and I was wondering if my conclusion makes scene. Most of the time that I can remember a 2wd will win over a similar 4wd car and I wanted some mathematical proof on why that is. I am not entirely sure where to begin this one...

Given:
(gross assumptions)
Both cars have the same mass, same moment of inertia for all four wheels, same wheel radius, both cars produce the same amount of power and torque. Both undergo rolling without slipping (just for simplicity) and assume that the coefficients of friction and rolling resistance is the same for all four wheels and between cars.

Find:
In a drag race over a set distance what car would achieve the highest velocity the fastest

Analysis: well I am kind of lost right now...but in essence my thinking is this...
sumtorques=Ia
2wd: T/2=Ia
4wd: T/4=Ia

So a 2wd car's wheels (and thus acceleration as atan*r) at a given power will be 2x that of a 4wd car...i feel like something is missing i made a free body diagram etc. but because the mu kenetic is the same on all four wheels and between cars the total loss for both cars is the same...help?

This is how I explained this problem to myself-

The wheels have a tiny moment of inertia, when compared to the mass of the car. And this means, you can assume the wheels are mass-less, like we are asked to in many simple mechanics problems.

So, the forces acting on the wheels are HUGE relative to the light wheels (while being quite normal relative to the mass of the car). For the kind of angular acceleration required at the wheels (reasonably small), the net torque on the wheels from the road = torque from differential (zero mass => almost zero force for non infinite acceleration).

Therefore, road torque = engine torque, at each driven wheel.

So at the end of this argument, the angular acceleration is insignificant, and what matters is the force on the wheels. So even though the torque is split as T/4, it gets converted into (T/4*radius at each wheel)*4 = total force. Which is the same as T/2*radius*2.

And since there's no torque from the differential at the non driven wheels, the road provides just enough torque to accelerate the (light) non driven wheels. And the corresponding force will have a tiny magnitude relative to the other forces acting on the car, and so can be neglected.

Obviously, converting the moments of inertia into equivalent mass is much more systematic and accurate, I haven't talked about traction limited and power limited acceleration, and I'm aware that you can't just neglect the mass of the wheels in problems. But this explains things kinda intuitively to an extent right?
 

What is the difference between 4wd and 2wd?

The main difference between 4wd and 2wd is the number of wheels that receive power from the engine. 4wd, or four-wheel drive, means that all four wheels of a vehicle have power from the engine, while 2wd, or two-wheel drive, means only two wheels have power.

Which is better, 4wd or 2wd?

The answer to this question depends on the individual's needs and preferences. 4wd is generally better for off-road or rugged terrain, as it provides better traction and control. 2wd is usually more fuel efficient and easier to handle on paved roads.

Is 4wd always necessary?

No, 4wd is not always necessary. It is only needed in specific driving situations, such as off-roading or driving in harsh weather conditions. In normal driving conditions, 2wd is sufficient.

What are the advantages of 4wd?

There are several advantages of 4wd, including improved traction and control on rough terrain, better ability to navigate through snow and mud, and increased towing and hauling capacity. It can also provide a sense of security and confidence while driving in challenging conditions.

Why does Jeremy Clarkson use 4wd as proof of a vehicle's capabilities?

Jeremy Clarkson, a well-known automotive journalist and television personality, often uses 4wd as proof of a vehicle's capabilities because it is a feature that can greatly enhance a vehicle's performance and functionality. He also values 4wd for its ability to handle challenging driving situations and push the limits of a vehicle's capabilities.

Similar threads

  • Classical Physics
3
Replies
95
Views
4K
  • Mechanical Engineering
Replies
5
Views
3K
Replies
69
Views
10K
  • Mechanical Engineering
Replies
4
Views
4K
  • Electromagnetism
Replies
10
Views
1K
  • Other Physics Topics
2
Replies
45
Views
57K
  • Mechanical Engineering
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Mechanical Engineering
Replies
15
Views
2K
Replies
15
Views
1K
Back
Top