The trail

Motorcycle geometry
The trail and the directional stability of the vehicle
Trail changing during a curve

The motorcycle geometry

Commonly when we speak about the motorcycle geometry we refer to the following three geometric parameters:

- the wheelbase;
- the castor angle;
- the trail.

Consider the vehicle in vertical position and with the steer rotation angle equal to zero. (fig.1).


Fig. 1 The motorcycle geometry

The wheelbase is the distance between the contact points of the tires with the road plane; the castor angle is the angle between the vertical axis and the rotation axis of the front frame (steering head); the trail is the distance between the contact point of the front wheel with the road plane and the point of intersection of the steer axis always with the road plane.
The geometric parameters shown in the figure above represent:


Fig. 2 Trail obtained with the inclination of the front fork. Front fork with equal (on the left) and different slope from the steer axis (on the right).

In most cases the trail is obtained inclining the steer axis (21-35°) and advancing the front fork and/or the front wheel respect to the steer head.
Theoretical it is possible realize the trail with a zero degree steer slope; this solution has got some disadvantage; in fact the front fork suffer a bigger stress and compression during the braking.


Fig. 3 Trail obtained withoff set of front fork and/or the wheel.

Now some consideration on the geometric values normally used are explain.
The next schedule shows the geometric values of some motorcycle.

(the values are been deduced by unofficial publications and so they me be incorrect)
Motorcycle
wheelbase

[mm]
e

[gradi]
a

[mm]
an

[mm]
load%

front/rear
Rn = an/bn %
Rp
kind of motorcycle
Kawasaki Muzzy -95-
1395
24.5
100
91
54-46
6.69
7.8
S.B. race
Ducati 916 -95
1428
24.5
100
91
51.5-48.5
6.54
6.95
S.B. race
Aprilia RSV250-95
1340
21
76
71
53-47
5.37
6.05
race
Aprilia RSV400-95
1368
21.
76
72.5
54-46
5.26
6.17
race
Yamaha 250-90-
1328
22.5
82
75.7
55-45
5.82
7.11
race
Honda NSR 500
1400
23
95
87.4
53-47
6.35
7.16
race
Honda VTR1000F
1430
25
97
87.9
47.5-52.5
6.35
5.74
supersport
Honda CBR 900 RR
1405
24
90
82.2
50.5-49.5
6.02
6.14
supersport
SUZUKI TL1000S
1415
23.7
93.5
85.7
47.5-52.5
6.20
5.61
supersport
Aprilia 1000rsv
1415
24.5
97
88.3
49.2-50.8
6.42
6.21
supersport
Suzuki GSX-R 750
1395
24
96
87.7
50.4-49.6
6.44
6.54
supersport
BMW R1100RT
1485
27.2
122
108.5
50.7-49.3
7.59
7.80
touring
Triumph Speed Triple T509
1440
24
86
78.6
48-52
5.64
5.21
touring
Moto Guzzi Centauro
1475
26
90
80.9
46-5
5.75
4.90
touring
Harley Davidson 1200 Sport
1485
29.6
116.8
101.6
45-55
7.29
5.96
touring
Laverda 750S
1375
26°
103
92.6
48.2-51.8
6.97
6.4
touring
Yamaha TDM 850
1470
25
105
95.2
49-51
6.71
6.46
touring
Buell S1 Lightning
1397
25
99
89.7
50.3-49.7
6.62
6.67
touring
Ducati Monster 90
1430
23
104
95.7
45.2-54.8
6.78
5.59
touring
Suzuki Vx800
1555
31
142
121.7
44-56
8.37
6.57
touring
Aprilia Motò
1460
26
108
97
45.5-54.5
6.89
5.75
touring
Yamaha XT600 E
1440
27.75
120
106.2
44.6-55.4
7.69
6.19
off-road
Honda XL600V Transalp
1505
28
108
95.4
47.4-52.6
6.70
6.03
off-road
Suzuki VS600 Intruder
1560
33.25
145
121.26
43.6-54.4
8.50
6.81
custom
Kawasaki VN800
1625
34
149
123.5
43-57
8.40
6.34
custom
Aprilia Classic 125
1553
32
100

 
45.5-54.5
60.5
50.5
custom
Moto Guzzi California
1470
28
88
77.7
46.4-53.6
5.65
4.89
cruiser
Bmw R1200c
1650
29.5
86
74.8
49-51
4.95
4.75
cruiser
Honda F6C 1500
1690
32.33
152
128.4
47-53
8.36
7.41
cruiser
Aprilia Gulliver 50
1255
25.5
55
49.6
42-58
4.2
3.04
scooter
MBK Flame 125
1220
27
78
37-63
37-63
6.0
3.52
scooter
Honda Foresight 250
1450
27.5
87
77.2
43.4-56.6
5.66
4.34
scooter

A parameter to make a comparison between the different motorcycle geometry can be the ratio between the front and rear normal trail:



The front normal trail is variable in the field of 4-8% respect to the rear normal trail.
The racing motorcycles have got the value of the ratio that is about 6%; the sporting and super sport vehicles have got the ratio that is from 6 to 6.5%; the touring vehicles have got the ratio that is from 6 up to 8%.
The motorcycles like cruiser (heavy vehicles ) are characterized by a ratio of 5-6%, then they have got little trail respect to the wheelbase. It is due, probably, to the need to have a good handling when the speed is low; since the load on the front wheel is high due to the heavy total mass of the motorcycle, the choice of a little trail reduce the steering torque applied by the rider to drive the bike. It is to observe that the normal use of these vehicles is at not high velocity and so it is not necessary a big trail that guarantee high stability at high speed.
For the same reason the ratio is little also for the scooter.
At rigour the ratio may consider the mass distribution on the wheels; a vehicle with a big load on the front wheel needs a lower trail. In fact big loads on the front wheel generate bigger lateral friction forces under the same slip of the wheel. Therefore, to obtain the same recall torque around the steer axis it is necessary reduce the normal trail.
The correct ratio in function of mass distribution on the wheel is:



Fig. 4 Vertical load and lateral force acting on the front wheel.

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>The trail and the directional stability of the vehicle

To develop this concept consider a motorcycle with a straight running motion at a constant speed. At a certain point it suffers an external perturbation (for example an irregularity of the road surface or a gust of lateral wind), that generates a little rotation of the steer on the left.
Leaving from the fact that the vehicle begins to turn on the left and then, because of the centrifugal force, it starts to roll on the right, concentrate the attention on the lateral friction force F generated by the contact of the tire with the road surface.
On the front tire is applied a friction force F that has got the same way of the slip, but opposite direction. Since the trail is positive, the friction force F generates a momentum that tends to put the steer in equilibrium. The torque is proportional to the normal trail (figure 5). Bigger is the normal trail, greater is the momentum that tends to put the steer in equilibrium at the same slip.


Fig. 5 Stabilizing action f the normal trail.

If the trail is negative (contact point between wheel and ground set forward the intersection point of the steer axis with the road surface), the friction force F, always opposite to the slip speed, generates a torque around the steer axis that increases the steer rotation on the left. The friction force F amplifies the perturbation effect, compromising the stability of the motorcycle (figure 6). amplifies the perturbation effect, compromising the stability of the motorcycle (figure 6).


fig. 6 destabilizing action of negative trail.

It is important observe that the trail may became negative for the road surface when the wheel across a step or a hump. This is frequent in off-road use. For this motive the off-road vehicles have a high value of the trail.


Fig. 7 Negative value of the trail generated by asperity of the road.

Now let we see what matter when the trail is zero. In this case the lateral force doesn't generate any momentum around the steer axis; the directional stability is compromise.


Fig. 8 Value of the trail equal t zero

In conclusion it is possible to say that:
- little values of the trail generate little straighten momentum; the consequence is that the steer is very light but the directional stability is modest. Small perturbations of the road surface generate steer rotation easily;
- big values of the trail generate elevated straighten momentum; the vehicle is stable but is necessary a bigger steer torque under the same trajectory.

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Normal trail changing during a curve.
Up to now we made consideration about normal trail measured with the motorcycle in vertical position and with steer rotation angle equal to zero.
The normal trail is important because the momentum due to the reaction forces (vertical load and lateral force) around the steer axis is proportional to the normal trail. In fact the forces acting on the tire (figure 9) can be divided in one force parallel to the steer axis and one force normal. The trail represents the arm of the normal component.

Fig. 9 Reaction forces that generate a momentum around the steer axis

At this point it is important to see how the normal trail changes when the vehicle is curving.
The figure 10 shows the variation of the normal trail when change the roll and steer rotation angle. It is evident that the normal trail decreases when the roll angle and the steer rotation angle increases. If we consider steer rotation angles lower than 5° and variations of roll angle lower than 40°, the variation of the trail is less then 20%.


Fig. 10 Normal trail in function of the roll and steer rotation angle

The figure 11 shows that the increment of the radius of the toroid of the tire attenuates these variations; with a steer rotation angle of 5° and a roll angle of 40° the variation is of 10%. The different front tire may change the radius of the toroid and then the arm of the reaction force during the curve.
Since the rider "feels" the behaviour of the front frame through the torque applied on the handlebar, it is evident that the variation of the toroid radius may change the feeling with the vehicle.


Fig. 11 Normal trail in function of the roll and steer rotation angle.

If the normal trail remains constant and the steer angle changes, doesn?t change the graphic in appreciable way, that is the normal trail during a curve is quite insensitive to the steer angle.
In conclusion it is possible declare that, in the comparison between vehicles with different characteristics, is preferable consider the normal trail.
For example in the figure 12 is shows the trail in function of the roll and steer rotation angle. It is possible to observe that, contrary to the case of normal trail, when the roll angle increases, the trail may increases too.


Fig. 12 Trail in function of roll and steer rotation angle.

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