Why does a car need more torque when accelerating from rest?

Since static friction helps in the movement of rolling motion, not opposes it, Why do we say we need more torque to get the car to move from rest if we have the rolling friction coefficient static and the torque = mass * acceleration * wheel radius, surely the mass and radius do not change. So, why do we need more torque at the starting of movement than at regular acceleration when the car is already moving?

• Cars are a lot more complicated than that. – JMac May 2 '17 at 20:15
• What do you mean? – user3407319 May 2 '17 at 20:16
• There are a lot more things than just the tires on the pavement resisting a car's willingness to start from rest. There is (generally) a combustion engine driving pistons which turn a shaft which delivers power to other components. Just because static friction of the tires stays the same doesn't account for the engine's process of delivering torque. – JMac May 2 '17 at 20:18
• I think the other components need the same torque regardless of the speed, right? – user3407319 May 2 '17 at 20:20
• The actual power component of the engine has to convert a chemical (gasoline) to torque. Making a process to get torque from that doesn't give you consistent power. – JMac May 2 '17 at 20:23

There are two factors I know of. First, and less important, overcoming static friction requires more force than kinetic friction. This applies to all of the internal parts that have to get going/moving past each other, and probably to the rolling friction of the tires.

The major reason, though, has to do with how cars based on internal combustion engines work. See, an internal combustion engine can only supply torque and power when it's already moving. That's why you need an electric starter motor to get the engine going when you start the car. Now think about if the engine were linked directly to the wheels by gears - that would mean if the car is stopped, the engine isn't running. To get over this problem cars have a clutch inside of them that transmits the torque from the engine to the gear box and drive shaft. When the clutch is fully engaged, all of the torque and power are transmitted. As it is in the process of engaging, though, only part of the power is transmitted. This is especially important when starting from rest because it is that partial engagement that allows the wheels to come up to a speed that the engine can supply torque at without stopping.

So, bottom line, the engine needs to be able to supply more torque at low rotation rates in order to get the car moving because not all of the power is being transmitted to the drive train by the clutch.

With an electric motor this is not a problem - they can supply 100% of their torque even at zero rotation.

• All torque is transmitted by the clutch... not all power is. If you need to slip the clutch to get the torque through, you lose a lot of power (heat/burn the clutch). – Floris May 2 '17 at 20:35
• @Floris Good point. Right ultimate reason, wrong description. I'll try to update it with the correct reasoning. Also, you do need to slip the clutch to get the torque through when you're starting motion. You want to minimize the time over which this happens to minimize wear, but some slippage is inevitable (else there'd be no need for a clutch). – Sean E. Lake May 2 '17 at 20:45
• @SeanE.Lake I don't think the first factor has a relevance because all parts inside a car rotate I guess, nothing moves horizontally in a car except the whole car itself, so static friction doesn't count here right? – user3407319 May 2 '17 at 21:24
• @user3407319 Think about what rotation of a part relative to a stationary part that is holding it entails. Imagine zooming in to where the rotating and stationary part meet. No, motors don't need gears. – Sean E. Lake May 2 '17 at 21:34
• Just because the clutch slips does not mean it doesn't transmit all the torque. Just think about conservation of angular momentum. Unless the entire engine block starts rotating... – Floris May 2 '17 at 23:55

The power you can transmit (force times velocity) depends on velocity. To get any power when velocity is small, you need a lot of force. And force is just torque divided by distance (distance = radius of wheel), times whatever scale factor the gear box supplies.

So all the horse power in the world won't move your car from standstill; only torque can do that.

• Yeah i know torque does the moving, but why does it need more torque at first when it is starting to move than you need when you are just moving and need to accelerate to a higher speed?? – user3407319 May 2 '17 at 20:27
• As I said - in order to take advantage of your power, you need torque at the low end. That's where a little bit of energy should provide a lot of acceleration (not a lot of kinetic energy needed) - so you are limited by the torque of the engine not the power. You can use "equal torque" but then it takes a long(er) time to accelerate. – Floris May 2 '17 at 20:32

I think this is a case of classical mechanics and in considering the problem, you need to think in terms of moments (force $\times$ lever arm). The tyre, in contact with the road, moved around a pivot (the axle). This creates a lever arm of approximately $300mm$. Given the weight of the vehicle, at say a metric ton, which is always being pulled down by gravity, the vehicle has a mass of $1000\times 9.81$. The combination of these implies that there is a moment generated in the wheels of $0.3\times 1000\times 9.81\approx 3000$ Newton$\times$ meters (Nm). This is the torque required to move the vehicle. That's 3kNm that has to be rotated-the torque, hence the torque required to get a vehicle moving from an at rest condition. Now, if we imagine the same vehicle has a velocity, conservation of momentum comes into play and the mass has an energy equal to $\frac{1}{2}mv^2$, again measured in $kg\times m^2/s^2$, hence other than rolling Road resistance and wind pressure on the front of the vehicle, pressing on the accelerator in a higher gear will further accelerate you.

The confusion is in the idea the car "needs" more torque. In order to accelerate at a given rate the rear wheel torque needed is essentially the same at 30mph as it is standing still. At higher speeds there's aero drag to overcome and you actually need more torque to accelerate than from standstill. But an internal combustion engine doesn't produce any torque at zero speed, and the torque it can produce is roughly constant from idle speed to a few thousand rpm. So to get significant torque at the rear wheels you have a gear box that, in first gear, allows the engine to turn fast enough, above idle, to make power when the wheels are turning slowly. Power from the engine to the wheels is a conserved quantity (minus a little for friction loss), while torque can be any value depending on the gear ratio. But even first gear doesn't allow the engine to make torque at zero rpm, so you have a clutch that allows the engine to turn above idle rpm even when the wheels are stationary. The clutch transmits torque, but it wastes some power.