I'm trying to understand the physics of why accelerating rapidly uses more energy than a more gentle acceleration?
Is the motor/inverter less efficient at high current?
Is the motor/inverter less efficient at high current?
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Written for gasoline cars, but the same principles apply....See #2
http://www.pepperdine.edu/sustainability/services/EcoDrivingUSA_EcoDriving_Practices.pdf
I'm trying to understand the physics of why accelerating rapidly uses more energy than a more gentle acceleration?
Is the motor/inverter less efficient at high current?
I'm trying to understand the physics of why accelerating rapidly uses more energy than a more gentle acceleration?
Is the motor/inverter less efficient at high current?
This.Resistive power losses in the battery pack, drive inverter, motor, and associated wiring are proportional to the square of the current. So doubling the motor current doubles the torque but quadruples the losses.
It depends on what your goal is. If your goal is to accelerate to a target speed (for example during a freeway on ramp) then the energy needed is just the kinetic energy (1/2*mv^2). Using the analysis of force, yes, the acceleration and force is higher, but the distance required for reaching that speed is lower.The energy applied to the car is the force (lb for Newtons) times the distance traveled under that force. Faster acceleration requires higher force far a given mass. This is somewhat of a simplification, but more energy is required.
The energy applied to the car is the force (lb for Newtons) times the distance traveled under that force. Faster acceleration requires higher force far a given mass. This is somewhat of a simplification, but more energy is required. Therefore, even if the motor efficiency is exactly the same it will still take more energy from the battery for faster acceleration.
Motor efficiency will also have an effect, and most motors will be most efficient at medium torques and speeds.
GSP
It depends on what your goal is. If your goal is to accelerate to a target speed (for example during a freeway on ramp) then the energy needed is just the kinetic energy (1/2*mv^2). Using the analysis of force, yes, the acceleration and force is higher, but the distance required for reaching that speed is lower.
Of course when you throw in other increased losses from higher acceleration, you still turn up worse (how much worse is unknown, esp. for EVs). Also those that accelerate fast tend to either overshoot their target speed (causing unnecessary energy loss by having to slow down again) or it leads to excessive braking (like between stoplights).
But at higher acceleration won't it be for a shorter duration? i.e. won't the total area under the curve still be the same? Slow acceleration will be a long, slowly increasing curve. Fast acceleration will be a steep, but short curve. Total area the same.
This is something I've wondered about as well. Assuming the motor is equally efficient at all power inputs, it should take the same amount of energy to accelerate a mass to a given speed, regardless of how fast. Faster requires more energy, but is done over a shorter period of time, so the net is the same.
I think the only difference then is attributed to lower motor efficiency at greater power inputs, where more energy is lost to heat. That, and also the real world tendency to overshoot the target speed when accelerating fast, which will be wasted energy.
It depends on what your goal is. If your goal is to accelerate to a target speed (for example during a freeway on ramp) then the energy needed is just the kinetic energy (1/2*mv^2). Using the analysis of force, yes, the acceleration and force is higher, but the distance required for reaching that speed is lower.
Of course when you throw in other increased frictional and heat losses from higher acceleration, you still turn up worse (how much worse is unknown, esp. for EVs). Also those that accelerate fast tend to either overshoot their target speed (causing unnecessary energy loss by having to slow down again) or it leads to excessive braking (like between stoplights).
But at higher acceleration won't it be for a shorter duration? i.e. won't the total area under the curve still be the same? Slow acceleration will be a long, slowly increasing curve. Fast acceleration will be a steep, but short curve. Total area the same.
This is something I've wondered about as well. Assuming the motor is equally efficient at all power inputs, it should take the same amount of energy to accelerate a mass to a given speed, regardless of how fast. Faster requires more energy, but is done over a shorter period of time, so the net is the same.
I think the only difference then is attributed to lower motor efficiency at greater power inputs, where more energy is lost to heat. That, and also the real world tendency to overshoot the target speed when accelerating fast, which will be wasted energy.
An ICE has considerably greater inefficiencies at higher power inputs due to difficulties in maintaining adequate air intake as well as increased friction losses at the pistons and crank, resulting in lower efficiency at higher acceleration. An EV has none of these problems.
I tried to use a simplification, but I think if you integrate force over the same distance you still get more energy required for the more aggressive drive cycle.
GSP
The energy required to accelerate the mass in both scenarios is the same; however, the energy from the battery required for a higher rate of acceleration is higher due to the lowered conversion rate, as discussed above.