This is a mechanical drawing of a typical car engine. If you know car engines, you can see that this is a double overhead cam, 24-valve V6. There are two lobed camshafts that serve to open an close a pair of intake and exhaust valves per cylinder. There are six cylinders in a V shaped configuration as compared to in inline configuration which also exists.
When you look around these days, we have two main forms of propulsion that drive the vast majority of our vehicles around the planet - internal combustion engines and electric motors. The latter are becoming more commonplace than even a decade ago, but are still greatly outnumbered by the former.[br][br]While it might seem that it should be simple to substitute an electric motor for an internal combustion engine, it turns out that the way they deliver the force that propels a vehicle is very different.
An internal combustion engine burns either gasoline, diesel or something similar (like E85) in order to produce heat which causes air to expand against a piston which in turn rotates a crankshaft which goes through a transmission and eventually to the wheels. You know what it means to start an engine. If an internal combustion engine isn't turning, it is off. In order to produce any force, it must be turning. The higher the engine speed, the more combustion events per second take place, and the larger the force it can deliver to propel a vehicle. While this is true over a wide range of engine speeds, ultimately what puts an end to this growth of force with engine speed is that the engine needs to "inhale" air to mix with the fuel for combustion, and then needs to "exhale" that same air with spent fuel out the tail pipe. It is the flow of air through small intake ports and exhaust ports that becomes very difficult at high engine speeds. Quite literally the energy of combustion ends up being entirely wasted on the intake and exhaust of air at too high an engine speed and none is left over to propel the vehicle down the road. [br][br]These two effects in combination tend to lead to a force curve that rises linearly at first, but then peaks and dies off with engine speed. An example can be seen below. The lower curve is labeled as "torque", which is the effective twisting force of the crankshaft. While it comes out of the engine as a torque, or twist, when the rubber hits the road it is just a force to propel the car. Don't understand this to mean that torque equals force. It doesn't. But after the torque turns gears and drive shafts and wheels, what we get is a force that is proportional to the torque. The effect of gearing is discussed later.
Graphic from MotorTrend magazine: Notice the shape of the torque curve (the lower curve) that rises roughly linearly at first until the flow of air through the engine becomes an impediment and causes a decline.
If we wanted to define a function that looks like this torque curve, we could use a polynomial function to fit to the curve. That is the most common thing to do. The simplest function that seems like it might fit the curve is a downward facing parabola. In GeoGebra, photos can be imported. The image of the torque curve could be entered and scaled correctly. Then points could be created that fall along the curve, and a polynomial curve fit could be performed. An example of such a process is seen below. The points can be moved and the effects can be seen in real-time on the curve fit.
An electric motor uses the energy stored in batteries or from a power grid to generate electric and magnetic forces which in turn create rotation that serves to turn gears and drive a vehicle. The characteristics of the force generated are very different from those generated by an internal combustion engine. [br][br]The maximum force generated by an electric motor occurs at zero speed. The faster it goes, the less force it can generate. The reason for the decline with speed is for completely different reasons that in an internal combustion engine. We will have more discussions about electric motors during second semester, but here are the basic ideas: Electric motors are also electric generators because of the way natural law works. We can use the voltage from batteries to turn a motor, and turning a motor will generate a voltage. The trouble is that the generated voltage is always fighting the effects of the battery. The faster the motor turns the more it fights. At a high enough speed the generated voltage completely cancels the battery's voltage. This is called the no-load speed of a motor. The motor can not turn any faster than this on its own.[br][br]The upside to this effect is that the faster the motor turns, the less current and energy it draws from the battery - something which we'll work out in our studies of electromagnetism. On the other hand, at zero speed the motor draws maximal current and energy from the battery. This is in direct contrast from internal combustion engines which can't burn any fuel when they aren't moving, and burn it quicker the faster they are running.[br][br]The specific shape of the force versus speed curve for an electric motor is shown below. It is very nearly linear. The y-intercept is the stall torque, which relates to the maximum force it can generate, or stall force. The x-intercept is the no-load speed discussed above.
The effect of gears that sit between a motor and the wheels is to make a trade off between force and speed. The product of force and speed is determined by the motor. If you need more force, it will always be at the expense of lower speed potential. If you wish to go faster, it will have to be at the expense of having a lower force with which to accelerate and push the wind out of the way.[br][br]This is true in general, not just for electric motors. If you wish to experience huge force with which to accelerate a car, it will be in first gear. While the force is large, the gear probably can't propel the vehicle beyond 35mph or so - depending on the vehicle. Second gear will get you going faster, but at the expense of having a weaker force with which to propel the car along.[br][br]The graphic above shows this effect on the force curve. You can change the stall force and see its effect on the no-load speed.