Driving Simulator - Roll On the Power
Fast or Quick?
The fastest way through a turn is to brake in a straight line, drive an arc of constant radius to the exit, and then accelerate in a straight line. But this line, known as the reference line, is far from the quickest line. By giving up a bit of speed while cornering the driver can accelerate before reaching the exit. This produces a higher exit speed and a quicker sector time. Every known racing driver does this: only mathematicians use the reference line because it is easy to analyze.
Rolling on the Power
Real racing drivers roll-on the power (accelerate) before reaching the exit of the turn. This is often called “getting to the throttle” and is usually accompanied by unwinding the steering. Drivers do this naturally, but we need a way to quantify this for a computer program.
Let the driver roll-on the power with 30 degrees remaining in the turn. After the car has rotated 150 of the 180 degrees the driver will begin applying throttle. He will begin with 20% of maximum acceleration and increase to 90% at the outside exit.
Drivers do not have a compass to measure the attitude of the car. In reality the driver begins to roll on the power when he reaches a certain point on the track or when “it looks right’” Computers do not respond well to “it looks right” so we must define a numerical way to specify when the driver begins to roll on the power. We do this with the attitude of the car. An angle of 0.0 means the car has reached the end of the corner and it pointing down the exit straight. 10.0 degrees means the car has rotated all but the last ten degrees. This effectively moves the inside apex later from 90 degrees to 85 degrees.
This reduces the sector time to 13.299 seconds, a gain of 0.318 seconds. The Exit Speed rises to 110.734 (3.8 mph faster) in spite of the minimum speed falling to 61.357 mph. The Braking Point falls to 395.2 (the driver goes 1.5 feet deeper) and the Turn-In Point becomes 40.0 (4.0 feet deeper) at a speed of 61.357 mph.
The user can roll on the power even earlier. This improves the sector time up to a point. The table below shows sector times for rolling on the power with 30 degrees remaining, with 60 degrees remaining (getting to the throttle earlier) and 75 degrees (getting to the throttle very early). The first two columns refer to a 500-foot exit straight. The next two columns (Extend-1) refer to a 2500-foot exit straight. The final two columns refer to a 5,000-foot exit straight.
#
Acc/Dec Sector Time/Speed Ext-1
Time/Speed Ext-2
Time/Speed
1
0/ 0 13.616 106.939
23.384 163.570
33.003 187.801
2
30/ 0 13.299
110.734 22.925
164.567 32.508
188.209
3
60/ 0 13.144
114.684 22.623
165.668 32.167
188.663
4
75/ 0 13.300
117.066 22.691
166.363 32.211
188.951
The essential issue is that choosing a lower turn-in speed and roll-through speed generates an arc with shorter radius. This is traveled at a lower speed but the shorter radius leaves room in the exit of the turn. This permits the driver to get to the throttle sooner and generate higher exit speed. Also note that the very late apex produces the highest exit speed but not the quickest sector time - even with a 5,000 foot straight following the turn.
The highest exit speed does not produce the quickest sector time, even with a long exit straight.