Contour Enthusiasts Group Archives Forums General Autocross and Open Track Speaking of hairpins...

I remain uncertain about the best way to do a hairpin turn. So last night I did some SWAG calculating.

Picture a single-cone 180 degree hairpin. Now think of three different radius turns going around that hairpin. The first is a 20' radius, about the limit of turning radius at any kind of speed...we'll say 20mph or 29.3 ft/second. The second is 40' radius, taken at say 30 mph or 44 ft/second. The third is 60' radius taken at 40 mph or 58.7 ft/second. Dong the 2 pie r thing gives you circumference, and the half circumference distances are, drum roll:

20'radius = 62.8' distance
40'radius = 125.5' distance
60'radius = 188.4' distance

Now we apply the AVERAGE SWAG speeds to each distance (realizing that there is trail-braking going in and acceleration coming out) and we get:

20' radius half-circle @ 20 mph/29.3ft/sec = 2.14 seconds

40' radius half-circle @ 30 mph/44 ft/sec = 2.85 seconds

60' radius half-circle @ 40 mph/58.7ft/sec = 3.2 seconds

But wait, the widest diameter half-circle requires a turn-in point 40 feet earlier than the smallest half-circle. Choosing a smaller diameter half-circle still means you must traverse that distance in a straight line. Braking takes less time than acceleration, so we add .8 seconds for braking that extra 40', and 1.3 seconds to accelerate that extra 40' coming out of the turn. Add .4 seconds to brake the extra 20' for the middle diameter half-circle and .6 seconds to accelerate the extra 20'.(Wish I could draw this for you).

Results:

20' radius half-cicle + straights in and out=
4.24 seconds

40' radius half-circle + straights in and out=
3.85 seconds

60' radius half-circle (at 40 mph)= 3.21 seconds
60' radius half-circle (at 36 mph)= 3.57 seconds

I know, it looks like the smallest half-circle is the slowest and biggest half-circle is the fastest. The unknowns are who would have the higher exit speeds at the same line in space coming out of the turn. After all you can accelerate much faster in a straight line, while the car in the largest diameter turn is cornering and accelerating.

In addition, I contend you can brake later going into the tight turn because the bulk of the distance during braking is at higher speed. At slower speeds you can brake over much less distance. In other words there is not a direct distance ratio braking from 60mph to 40 mph for the wide radius turn versus from 60 to 20 mph for the smallest turn. The extra time spent at 60mph/88feet per second before braking SAVES you mucho time. But no time to discuss that here. Errors in my logic???? Help???? Off to work.

EDIT: Look at Road and Track figures for 80-0 and 60-0 braking. Think they are linear in proportion to speed? Think again. If a car requires 130 feet to brake from 60 mph, you can count on adding another 100' for the extra 20 mph. I would like to see braking figures for 40 mph and 20 mph going to zero. They would definitely be much, much less. In addition you can't just stand on the brakes to slow from 60 to say 40. You will screw up the weight transfer. The time spent transitioning, (i.e. trail-braking) at less than max pedal is lengthy and a smaller proportion of overall braking from say 60 to 20mph than say 60 to 40 mph. I contend you could brake a fraction of a second later going to the lower speed in the scenarios above.