Force vs power or torque vs power is a difficult concept for many people to understand. Most people who have an interest in cars will have an idea but have a hard time explaining it.
In our Superman vs the Flash analogy, Flash is the only person who is faster than Superman but Superman is capable of generating far more force than the Flash. We know that F=ma which means a=F/m so we should expect Superman to always win in a race. More force equals more acceleration equals greater speed. Right?
So why does Flash win in a race if Superman is capable of generating far more force than Flash? Is this just comic land ignoring real world physics or is thus scenario possible in real life?
The answer is in the relationship between force, work, energy and power.
If I apply force to an object and get it moving I am doing work on the object. The amount of work I do on the object is equal to the force I apply times the distance I apply the force (W=fd). When I do work on an object I change its kinetic energy by the amount of work I do on the object. Let’s say I apply one Newton of force on an initially stationary 1 kilogram mass for a distance of 1 meter. Ignoring gravity and losses due to friction I will do one Joule of work on the mass and, hence, raise its kinetic energy to 1 Joule. Since we know the mass of the object is 1 kg we can determine its final velocity with the formula KE=1/2 mv^2. The velocity of the mass is now roughly 1.4 meters/sec.
The final velocity of the mass is directly related to the amount of work I do on the object. If I do that work in 1 second or 2 seconds it doesn’t matter, the final velocity will remain the same.
This is where power comes into the discussion. Power is the rate at which I do work on an object, i.e. P=W/t. If I do 1 Joule of work on an object in 1 second I will be applying twice as much power than if I do 1 Joule of work on the object in 2 seconds. In the first case my power output is 1 watt, or 1 joule/s, because I increased my energy level to 1 joule in second. In the second case my power output is only 0.5 watts because I increased my energy level by 0.5 joules for two seconds for a final energy level of 1 joule.
Think of power as the ramp up rate of energy and the amount of energy I give to an object determines how fast the object will end up moving. Power is how fast I increase the energy of the object.
Okay this is still confusing because if I apply more force to an object I give it more acceleration and it gets up to speed that much faster so more force still means a greater increase in energy in a shorter amount of time. How is force different from power? And why do I care?
This is where the car buffs say, “But the amount of force (torque) my vehicle can apply to the road varies with how fast my vehicle is moving. The faster my car is moving the less torque it can exert.”
Bingo!
When we measure a person’s strength we measure how much force they are able to exert against an unmoving or slow moving object. When we measure a person’s power we look at how much force they are capable of exerting against an object that is in motion. We measure that value at various speeds and generate a power curve, i.e. how much force can I exert on an object that is moving at various velocities.
A typical power curve for a person can be found here:
Muscle Force Velocity Relationship
This is similar to the automobile analogy where a truck built for towing can exert far more force than a race car on a stationary or slow moving object but the race car is capable of far greater speeds. This is because the amount of force the truck is capable of exerting with its tires on the road (i.e. torque) decreases rapidly as its speed increases. The amount of torque the race car exerts also decreases as its speed increases but not as rapidly as the truck. At speeds of a little over a hundred miles per hour most trucks are only capable of exerting enough force to overcome drag and friction in order to keep the truck moving at a constant speed. The race car on the other hand continues to exert sufficient force to overcome drag and friction and to continue accelerating up to speeds in excess of 200 mph. When the race car reaches its maximum speed it too will top out and will only be able to continue at that speed without further acceleration.
Since power is equal to force times velocity (P=Fv) , at lower speeds the truck has more power but at higher speeds the race car has more power.
When it comes to casting we have another factor to consider. The time it takes to reach peak force. I may be physically much stronger than someone else but if someone else is faster than I am they will reach their peak force more quickly than I will. In casting we want to reach peak force quickly and then continue to apply a constant force to the rod for the duration of the casting stroke until we stop the rod butt. This was described by Bruce Richards in his article about Casting Analyzer Traces. If we take too long to reach our peak force the resulting casting analyzer trace will show a lack of “smoothness” resulting in tailing loop.
For most casting that we do we are capable of reaching the desired force for our casts quickly enough to be smooth and we have sufficient power to generate the line speed we need. These items are more of interest to distance casters or anyone looking to increase their distance cast.
How does one increase power and improve time to peak power for distance casting? I think that is a subject for a separate post which I plan to work on later.