They’re directly related to each other, not disparate properties.
Yes, they're related. They're not the same thing.
Torque times engine/motor speed times some conversion factor = horsepower
Numerically, horsepower = torque (in ft-lbs) * rpm / 5250.
If you have zero torque at any engine/motor speed you will also have zero horsepower at that speed.
Sure, what's your point?
If you have x torque and y horsepower at some engine/motor speed and x torque at twice that speed there will be 2y horsepower at the higher speed. If torque is double at the higher speed there will be four times the horsepower at the higher speed.
Your math skills are good.
Electric motors have more torque at lower speeds thus have more horsepower at those speeds.
That's true, but fairly irrelevant. Think about riding a bicycle. Accelerating away from a dead stop, the limiting factor is how hard you can push on the pedals. You're up against your torque limit. Low gears help by multiplying the torque at the rear wheel, by increasing the mechanical advantage...but, of course, limit your top speed by the same factor.
But when you're hammering at top speed on the flat, your limit isn't how hard you can push on the pedals. You can push even a fairly tall gear easily in terms of leg strength. Your heart and lungs (your aerobic capacity) are the bottleneck, not your leg muscles. You're no longer torque limited, now you're power limited.
Any vehicle has to face the same TWO limits -- a torque limit and a horsepower limit. At any given time, one is usually irrelevant because the other dominates. In general, at low speeds, you're torque limited, at high speeds, you're power limited.
One final consideration is that ICEs, by their very nature, take in and combust more fuel/air mixture as rpm increases. A four-cylinder engine idling at 600 rpm has 20 power strokes per second. At 6000 rpm, it has 200 power strokes per second. All other things being equal, that will result in 10 times the power output, and (at the motor output) 10 times the torque. And indeed, our experience tells us that ICEs really come alive as rpm increases. So at low rpm, where road speed is low and you need lots of torque, the ICE just doesn't have any. You need lots of gearing advantage to get out of the hole. But as speed (and rpm) increases, available torque and power skyrocket. That's just the nature of an engine whose power is produced in pulses which occur in proportion to rpm.
By comparison, an electric motor has full torque literally down to 0 rpm. That's still 0 power at 0 rpm, but you don't need horsepower down there. You need torque, which an electric motor provides in spades. But at high rpm, since the electric motor's available torque doesn't rise like the ICE's does, the horsepower curve flattens and turns downward while the ICE's is just coming into its band.
Bottom line, ICEs rule in top speed, EVs rule in low-speed acceleration. Obviously the transition speed varies based on a lot of variables, but my SR feels like it far outperforms my old ZX-11 in freeway roll-ons. The transition speed must be pretty high.
Long story short: Torque is good, torque is what accelerates you. Power just pushes air out of the way at high speed.
