## Stopping Distances Revisited.

In May of 2009, we posted a blog entry quoting the UK Survival Skills site on the subject of following distance. We also mentioned a pair of studies on brake reaction time and brake decelerative force from the Montreal Promocycle Foundation. Everyone seemed to be concluding that the two-second rule for following distance is not enough.

While the Survival Skills numbers looked pretty tough, we thought that the 0.9 G decelerative force and 0.5 second biker reaction time looked a bit optimistic in the light of the Montreal data. The performance of brakes is usually expressed as the fraction of a negative G (the force of gravity, which is 9.81 meters per second per second or 32.17 feet per second per second). This would mean that if we were braking with a force of minus one G, we'e be losing 32.17 fps of speed every second, which is roughly 22 mph.

From the brake reaction time paper we established an average reaction time of 0.62 seconds. The Montreal guys found that, on average, 95 percent of their research subjects could hit the brakes within that time interval. From the brake decelerative force paper, we took -0.774 G (just over three quarters of a negative gravity) as the average braking force for non-ABS bikes. Bear in mind that these were done with mechanically optimal bikes, experienced riders, flat dry and well-paved surfaces, in other words, unless you are very good or have ABS, things probably don't get much better than that.

The simple mechanical formula for speed under acceleration is v = u + f * t, where v is final speed, u is initial speed, f is acceleration force and t is the time. Taking v, the final speed as 0, we get **tb** = - u / f, where **tb** is the braking time once the brakes are applied.

The formula for distance is s = u * t + 1/2 * f * t^2, where s is distance, u is initial speed, t is time, f is accelerative force as before and the "^2" notation means 'squared'. We'll adapt this a little as s = u * (**tr** +** tb**) + 1/2 * f *** tb**^2, where** tr** is reaction time and **tb** is braking time.

This means that the first term uses the braking time and reaction time to measure the distance that would have been traveled without braking, and the second second one just uses braking time, as the reaction time plays no part in reducing the distance traveled due to the braking effect.

These are theoretical numbers, but they are based on real-world numbers measured from real-world bikers, and your personal numbers will surely differ. But you are not superman and the Nwetonian laws of mechanics do apply.

## Stopping Time and Distance, non-ABS

Speed - MPH |
Braking Time(seconds) |
Braking andReaction time |
Distance to Stop (feet) |

5.00 |
0.29 |
0.91 |
5.63 |

10.00 |
0.59 |
1.21 |
13.41 |

15.00 |
0.88 |
1.50 |
23.36 |

20.00 |
1.18 |
1.80 |
35.46 |

25.00 |
1.47 |
2.09 |
49.73 |

30.00 |
1.77 |
2.39 |
66.15 |

35.00 |
2.06 |
2.68 |
84.73 |

40.00 |
2.36 |
2.98 |
105.48 |

45.00 |
2.65 |
3.27 |
128.38 |

50.00 |
2.94 |
3.56 |
153.44 |

55.00 |
3.24 |
3.86 |
180.66 |

60.00 |
3.53 |
4.15 |
210.05 |

65.00 |
3.83 |
4.45 |
241.59 |

70.00 |
4.12 |
4.74 |
275.29 |

75.00 |
4.42 |
5.04 |
311.15 |

80.00 |
4.71 |
5.33 |
349.16 |

85.00 |
5.01 |
5.63 |
389.34 |

90.00 |
5.30 |
6.92 |
431.48 |

95.00 |
5.60 |
6.22 |
476.18 |

100.00 |
5.89 |
6.51 |
522.84 |

105.00 |
6.18 |
6.80 |
571.65 |

110.00 |
6.48 |
7.10 |
622.63 |

115.00 |
6.77 |
7.39 |
675.77 |

120.00 |
7.07 |
7.69 |
731.06 |

125.00 |
7.36 |
7.98 |
788.52 |

130.00 |
7.66 |
8.28 |
848.13 |

135.00 |
7.95 |
8.57 |
909.90 |

140.00 |
8.25 |
8.87 |
973.84 |

145.00 |
8.54 |
9.16 |
1039.93 |

150.00 |
8.83 |
9.45 |
1108.18 |

155.00 |
9.13 |
9.75 |
1178.59 |

160.00 |
9.42 |
10.04 |
1251.17 |

165.00 |
9.72 |
10.34 |
1325.90 |

170.00 |
10.01 |
10.63 |
1402.79 |

175.00 |
10.31 |
10.93 |
1481.84 |

180.00 |
10.60 |
11.22 |
1563.05 |

185.00 |
10.90 |
11.52 |
1646.42 |

190.00 |
11.19 |
11.81 |
1731.94 |

195.00 |
11.48 |
12.10 |
1819.63 |

200.00 |
11.78 |
12.40 |
1909.48 |

205.00 |
12.07 |
12.69 |
2001.49 |

210.00 |
12.37 |
12.99 |
2095.65 |

215.00 |
12.66 |
13.28 |
2191.98 |

We must emphasize, the Promocycle deceleration numbers were collected using experienced riders, bikes in excellent condition, on even ground, in the dry and on a good surface. And the bikes had training wheels. With different conditions your real numbers could easily be higher, e.g. a 3 percent downward grade would be worth an extra 5% and you could lose 20% due to reduced friction in the wet. There is a calculator from MSGROUP for stopping distance if you'd like to play more with these numbers.

We caculated numbers up to 215 MPH, just in case you have a 'busa. We are not recommending doing 215 MPH, we think you need to know that it'll probably take over 13 seconds and more than two fifths of a mile to stop, if you do.

The table below is the same set of calculations, but using the Promocycle average deceleration force for ABS as -0.869 G for bikes with ABS.

## Stopping Time and Distance, ABS-equipped bikes

Speed - MPH |
Braking Time(seconds) |
Braking andReaction time |
Distance to Stop (feet) |

5.00 |
0.26 |
0.88 |
5.51 |

10.00 |
0.52 |
1.14 |
12.94 |

15.00 |
0.79 |
1.41 |
22.30 |

20.00 |
1.05 |
1.67 |
33.57 |

25.00 |
1.31 |
1.93 |
46.78 |

30.00 |
1.57 |
2.19 |
61.90 |

35.00 |
1.84 |
2.46 |
78.95 |

40.00 |
2.10 |
2.72 |
97.92 |

45.00 |
2.36 |
2.98 |
118.82 |

50.00 |
2.62 |
3.24 |
141.64 |

55.00 |
2.89 |
3.51 |
166.38 |

60.00 |
3.15 |
3.77 |
193.05 |

65.00 |
3.41 |
4.03 |
221.64 |

70.00 |
3.67 |
4.29 |
252.15 |

75.00 |
3.93 |
4.55 |
284.59 |

80.00 |
4.20 |
4.82 |
318.95 |

85.00 |
4.46 |
5.08 |
355.23 |

90.00 |
4.72 |
5.34 |
393.44 |

95.00 |
4.98 |
5.60 |
433.57 |

100.00 |
5.25 |
5.87 |
475.62 |

105.00 |
5.51 |
6.13 |
519.60 |

110.00 |
5.77 |
6.39 |
565.50 |

115.00 |
6.03 |
6.65 |
613.32 |

120.00 |
6.29 |
6.91 |
663.07 |

125.00 |
6.56 |
7.18 |
714.74 |

130.00 |
6.82 |
7.44 |
768.33 |

135.00 |
7.08 |
7.70 |
823.85 |

140.00 |
7.34 |
7.96 |
881.29 |

145.00 |
7.61 |
8.23 |
940.66 |

150.00 |
7.87 |
8.49 |
1001.95 |

155.00 |
8.13 |
8.75 |
1065.16 |

160.00 |
8.39 |
9.01 |
1130.29 |

165.00 |
8.66 |
9.28 |
1197.35 |

170.00 |
8.92 |
9.54 |
1266.33 |

175.00 |
9.18 |
9.80 |
1337.24 |

180.00 |
9.44 |
10.06 |
1410.07 |

185.00 |
9.70 |
10.32 |
1484.82 |

190.00 |
9.97 |
10.59 |
1561.49 |

195.00 |
10.23 |
10.85 |
1640.09 |

200.00 |
10.49 |
11.11 |
1720.62 |

205.00 |
10.75 |
11.37 |
1803.06 |

210.00 |
11.02 |
11.64 |
1887.43 |

215.00 |
11.28 |
11.90 |
1973.72 |

The above numbers are only slightly better than the non-ABS figures, ranging from about 5 percent to about 10 percent for braking distance. In the risky business of motorcycle riding, a few percent edge often helps to make the difference between crashing and not crashing, so we think this is significant. We also note that the real benefit kicks in when the surface is loose or wet, and we think the braking performance of ABS-equipped bikes will degrade much less in adverse conditions. This is more research that needs doing, but we are encouraged by these numbers.

Once again, we're not suggesting that you ride your 'busa at 215, we're just saying, at whatever speed you choose to ride, ABS has a proven advantage.

## Relevance of these numbers.

You could point out that if you are following a cage, that you'll see the brake lights and have the time it takes the car to stop in addition to the following distance to stop in. That's true, most of the time. If the car takes a bend and slams into a jackknifed truck, or the car has a busted brake light switch, then you are out of luck. Many cars these days can pull more than -1G in braking force, so they can actually stop quicker than you can, thanks to the extra rubber and universal ABS on cars.

We don't see them as much in the US, but in the UK and Europe, huge pileups of hundreds of vehicles often occur on motorways in fog, so the danger is not totally theoretical.

We also note that the stopping time exceeds 4 seconds under 60 MPH, a moderate highway speed. This runs right up to the MSF's recommended 4 second immediate path rule. We refer to our TEAM OREGON blog posting, where we discussed their policy for space/time window allowances.

## Our revised recommendations

**Following Distance**: At least 3 seconds over 25 MPH, at least 4 seconds over 55 MPH, at least 5 seconds over 75 MPH, at least an additional 25% in the wet or on loose surfaces, and an additional 10 percent on downhill grades.

**Immediate Path**: 10 seconds (the MSF is 4 seconds)

**Sight Distance/Anticipated Path**: 20 seconds (MSF recommends 12 seconds)

We realize that, especially in cities, if you make a gap this large a car will jump into it, but we'd be looking for escape paths, and we note that 2 seconds is probably enough in dry conditions at city speeds around 24 MPH, but an extra half second would do no harm.

See Promocycle's research on optimal braking technique. We note that there were some instances of braking forces better than -1.0G during Promocycle's trials, and that 'covering' the brakes gave a reaction time bonus averaging about one sixth of a second. As the worst Promocycle observaton was worse than -0.4G, it is clear that there is a large range of effectiveness in braking, even with these experienced riders. It is possible to train up and improve your braking performance, and early alertness to the possibility of a need to brake in an emergency, with covering the brakes, will also produce a benefit.

As an example, if you trained up to 1.009 (the best Promocycle test) and were covering the brakes to reduce your reaction time to 0.47 seconds, your stopping time for 60 MPH would be reduced from an expected 4.15 seconds to a 3.18 seconds, and your stopping distance from 210 feet to 161 feet. Whereas if you hadn't got the brakes covered and braked with the worst Promocycle acceleration number of just worse than -0.4 G, your stopping time would increase to about 7.5 seconds and the distance to a whopping 355 feet. That sort of performance is unlikely to keep you out of any real-world trouble. And there's no reason why -0.4G is the downward limit, this is a bad attempt for an experienced rider, an inexperienced rider might do worse.

This requires skills. Effective braking requires maximum application of the front and back brakes without locking. Locking either wheel, while manageable, is potentially dangerous and will increase your stopping time and distance, which you can read about in the Promocycle papers. You can only maintain peak emergency braking performance by taking the time to learn the skill, and by practicing it on a regular basis.

Many of the experienced and advanced rider training courses in our Biker ED sections foster these skills. It is also possible to learn them by having someone show you, and to practice them on a range, in a parking lot or sometimes on the road, when conditions allow. Keeping brakes, tires and associated components well maintained and checked will help keep your bike's braking performance up. It's worthwhile making the effort to acquire these skills and keep them fresh. With motorcycle risk management, we'll take a few percent of edge wherever we can get them.