A couple weeks ago on YouTube John Cadogan made the statement “peak acceleration occurs at peak horsepower”, referring to typical IC engines.
I considered that ambiguous and not true in every situation, so I made a slightly less ambiguous statement in the comments.
Every Friday he does a video responding to some of the comments.
Today I managed to get an honorable mention (Skip to 12:55):
What he didn’t mention is that I further explained my viewpoint the previous week.
As follows (also in this weeks comments):
There are two possible scenarios:
Acceleration is proportional to the torque at the wheel. A = F / M (force applied divided by mass of the vehicle). F = T / R (torque applied to the wheel divided by radius of the wheel). Therefore A = T / (R * M). Since wheel torque is proportional to engine torque maximum acceleration occurs when the engine delivers maximum torque, when IN A FIXED GEAR.
After watching Nut-Fest 20 I see you are talking about a situation where VEHICLE SPEED IS FIXED (“any given speed”, as John says) and transmission ratio is variable. In this case picking a gear ratio that delivers maximum power from the engine also delivers maximum torque at the wheel.
I’ll walk through with some actual numbers, first ignoring rolling and wind resistance, on flat ground. Suppose the engine torque peaks at 4000 rpm, power peaks at 6000 rpm. The trans stays in 2nd gear. Engine 1000 rpm per 10 kph. Lets start at 20 kph & 2000 rpm and floor it. Car accelerates stronger and stronger (can be measured by an accelerometer) until it reaches 40kph. Acceleration in 2nd gear is strongest at 40 kph. Then acceleration starts to taper off. At 60kph still accelerating, but not as strong as at 40kph. No other gear ratio can give stronger acceleration at 60 kph because engine is at peak power.