How do you guys manage to drive in normal mode without getting shot

@ Corwyn "Linear" in the sense that there's no surges or gaps in acceleration. I get the impression that a (acceleration) is nearly constant for delta v (change in velocity) for speeds less than 80km/h / 50mph. Just my impression, mind you.
Imagine a car with manual transmission and a slow change. It would have different values of a as it went up the rev range as torque and power increased, then a=0 (or even a<0) for a fraction of a second during the gear change, then a at a similar rate and so on. An inattentive Prius driver would bounce of its bumper every time the other driver changed gear.

 

As long as we agree that that isn't what "linear" means.

Acceleration IS delta v (sort of).

You may be wanting to say that acceleration is smooth and continuous. Or even, constant. Both those with respect to time. Of course, that depends on what one is doing with the gas pedal over that time.

Given that, where were you going with that comment?

 

I've been trying to figure this out, but I'm guessing the intent with "linear acceleration" was to suggest that there is a one-to-one relationship between increase in speed and change in time.

Constant acceleration obviously produces a non-linear result in velocity (shall we say "speed"?), so a "linear acceleration" would take considerable engineering to accomplish, as the rate of acceleration would have to decrease along a curve in just the right way to allow the one-to-one delta v to delta t.

With all of that said, I'm really not remembering where this was going. Even so, I do like the very smooth acceleration afforded by the HSD with the planetary gear.

 

Hmmmm, ever notice how anyone driving faster than you is a lunatic, and anyone driving slower is a moron?

 

The greater the difference in speed between the slowest vehicle and the fastest in traffic, the greater is the chance for accidents.

 

By always being courteous!

 

If acceleration is constant (call it A), and since velocity is integral of acceleration over time(t), the integral of A is: V = At + C, which is the general form of the equation for a line. So constant acceleration obviously produces a linear resulting velocity.

Linear acceleration would be an acceleration of At + C, which would, of course, give a velocity of At^2 + Ct + D. The curve of acceleration would be a straight line (hence linear). Not sure what you mean by one-to-one delta v to delta t.

 

Here, I've done it again. I'm using the some of the right terms the wrong way. I'll try to improve only by explaining what I'm trying to say. You've done a much better job than I in explaining the basic calculus, so I'll go with your statements. Unfortunately for me, I don't see how this works in the real world where resistance, both road friction and air drag have non-linear negative effects on velocity.

I'll offer again my belief that you cannot have linear acceleration without some rather significant adjustments, as you will need to have non-linear power increases over time in order to counter the non-linear increases in friction and drag at higher speeds.

Further, I'm not really certain where this is going -- except to show that I've done a lousy job of trying to explain a basic view. (Like my "one-to-one delta v to delta t" -- which is a very poor way of saying acceleration is a mathematic relation between velocity and time.)