Acceleration 101

[Control Freak]

I’ve heard several questions about torque verses horsepower and the impact on acceleration. We also have a thread discussing the use of very simple equations to predict vehicle acceleration. I decided to put this thread together to explain various things that impact acceleration and how they are addressed. So here it goes.

 

Let’s start with Newton’s Law, Force = Mass x Acceleration. Moving things around Acceleration must be equal to Force/Mass. Mass is the same as weight here, so given the same force a lighter car will accelerate faster. The force in this case is the tractive force the tire exerts against the pavement to propel the car forward. The first figure below is a rough graph of tractive force I will use to explain. Anything that can be done to raise the tractive force line will increase acceleration. So, let’s step through the graph and look at what limits us at each point.

 

The first section is the flat part of the line. This is the overall tractive force limit of the tires. Above this point the tires break free and spin. In fact, when the tires begin to spin their ability to produce tractive force decreases greatly. This is why when you break your tires free you must throttle back well beyond the point they broke free in the first place in order to regain grip. There are two ways to increase the tractive force in this range. One is to distribute the power over more wheels. Each wheel many have the same tractive force limit but they will all add up to more overall force. This is where AWD helps. Unfortunately, AWD also adds some weight, which works against us. A much simpler solution is to make the tire contact surface bigger. This is what is done with dragsters because it doesn’t cost as much weight. Of course, this solution won’t work in snow and ice so we’re back to AWD.

 

In the second section we are horsepower limited. Basically, wheel torque is proportion to tractive force and Torque x Speed = Power. Therefore, as speed go up the ability to produce wheel torque goes down given a constant power level. However, horsepower changes with engine speed. So there are two things that can be done here. First, simply increase the horsepower level across the board by adding more displacement. A second option is to increase the torque at lower rpm so you get more horsepower down low. This is also referred to as increasing the power band and can be done through modifications to the air path, turbo, and ECU. A comparison of a good power band verses a bad power band can be seen in the second figure below.

 

At the third section, horsepower begins to drop off as the redline approaches. Here we must shift up so the rpm’s drop and the engine moves back to its peak horsepower band. Alternatives here include increasing airflow by modifying the air path, upgrading cams, and/or increasing turbo boast. Of course, even if we keep the horsepower from dropping off we’re facing the redline. Now, it becomes a matter of increasing the rpm capability through component upgrades like new pistons, bearings, conrods, and the list goes on.

 

Once we shift sections two and three are repeated until we’re at the desired speed/distance or we’re out of gears. Then it becomes a question of top speed verses acceleration, which can be addressed at another time.

 

Now the case I’ve layout out here is starting from a stand still. When cursing we’re operating on some line below the one I’ve drawn. Here we must push the engine up to the operating line on the first graph. A simple way of doing this may be to downshift. However, a single downshift may not be enough. In fact a double downshift many not be enough if we’re far enough below the line I’ve drawn. In that case we must just wait for the engine to spin up. Here a lightweight flywheel or other modifications that reduce the engine rotational inertia help.

 

In general peak torque is reached at a much lower rpm than peak horsepower. Therefore, a higher peak torque is an indication of a better power band. To an extent a poor power band can be compensated for adding more gears and dropping the clutch at higher rpm’s. This is the case with the RX-8. It only has 158 ft-lbs of torque but accelerates 0 to 60 in 5.9 seconds. However, it takes dropping the clutch at 7000 rpm’s and rowing through a lot of gears to do this. It also has the odd characteristic of having a much worse 5-60 time.

 

This is not all completely comprehensive. Of course, some modifications many work on some engines that don’t work on others. Hopefully, it was worth reading though.

[AreEyeSeeKay]

Great Post...One question though. [quote] A much simpler solution is to make the tire contact surface bigger. [/quote] Since Friction force is usually independent of surface area, what goes on when you make the tire surface larger? I imagine the coefficient of friction must be increasing, but i can't figure out why.

[Th3Franz]

[quote name='AreEyeSeeKay'] Since Friction force is usually independent of surface area, what goes on when you make the tire surface larger? I imagine the coefficient of friction must be increasing, but i can't figure out why.[/quote] The more physics classes I take, the more I try to figure this out..

[Control Freak]

Well there are a couple factors here. First, the width allows you to go to a softer compound tire. As the tire gets wider the force the rubber must transmit is distributed over a larger area and therefore the stress level goes down. With a lower stress level the rubber doesn't need to be so hard and a softer rubber has a much better coefficient of friction. Second, with very soft rubber you can actually start to squeeze the air out between the tire and the road. This begins to create a suction effect.

[RSPDiver]

One think to consider about tire size and profile is that a wide low-pro tire will fare much better in lateral traction, while a thinner taller tire (with a more oval front-to-back contact patch) will assist in acceleration. Take top-fuel drag tires for instance. They have HUGE sidewalls, and elongate with speed. That is to provide the max grip for forward motion.

[coolbluelb]

[quote name='RSPDiver']One think to consider about tire size and profile is that a wide low-pro tire will fare much better in lateral traction, while a thinner taller tire (with a more oval front-to-back contact patch) will assist in acceleration. Take top-fuel drag tires for instance. They have HUGE sidewalls, and elongate with speed. That is to provide the max grip for forward motion.[/quote] The high profile on top-fuel cars serve the purpose of reducing tire RPM. Spin any tire fast enough and it will come apart; tall tires cover more distance per revolution.

[RSPDiver]

[quote name='coolbluelb'][quote name='RSPDiver']One think to consider about tire size and profile is that a wide low-pro tire will fare much better in lateral traction, while a thinner taller tire (with a more oval front-to-back contact patch) will assist in acceleration. Take top-fuel drag tires for instance. They have HUGE sidewalls, and elongate with speed. That is to provide the max grip for forward motion.[/quote] The high profile on top-fuel cars serve the purpose of reducing tire RPM. Spin any tire fast enough and it will come apart; tall tires cover more distance per revolution.[/quote] Right, but that has nothing to do with traction. My point was to the traction benefit of an elongated (front-to-back) contact patch, utilized extensively in large drag tires which have very thin (2 ply) sidewalls, whose contact patches become longer and thinner when rotating.

[Drift Monkey]

Wow, very informative post! If anyone didn't understand Acceleration, now they do! 8)

[rockon]

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