HOW
ENGINE TORQUE AFFECTS THE SUSPENSION
By
Rick Johnson of TOO TECH RACING
Rick graduated from General Motors Institute in 1977.
He has worked with Dirt bike Suspension since 1982.
He raced the local Pro class in the 80’s and still rides and competes
regularly in the over 40 Master A and Pro classes. Rick continues to perform
shock-tuning trackside at a variety of Southern California Tracks.
BACKGROUND
There seems to be a lot of confusion regarding how tension in the chain affects a motorcycle suspension. Contrary to many track side opinions, the tension in the chain during acceleration does not cause the rear end to sag, but instead, actually reduces the frame’s tendency to squat. To prove this, perform this simple experiment: Put your bike in 1st gear directly in front of some immovable object such as a tree. Rev up the motor and slowly let out the clutch loading the motor. Notice how the rear fender rises under this load.
The net squat that one sees between the rear wheel and the fender during
acceleration is caused from the vehicle’s weight being transferred to the rear
wheel and the rear spring deflecting under this increased load.
Riders use chain tension to their advantage. For instance, if you gas it as you go up a jump ramp the bike will fly higher and farther. If you chop the gas as you go off a jump the bike will stay lower and not go as far in the air. This is all because of tension in the chain. Read on for the technical explanation of chain tension and how it affects bike action.
What effects I will explain: To better understand the effects of
chain tension, we will look at the forces the chain exerts on the rear wheel and
frame, how these forces affect suspension performance, and then discuss how the
rider can use these forces to his advantage on the track.
Then we will discuss the pros and cons of the ‘Torque Eliminator”
product’s ability to eliminate these chain reactions.
We will choose some numbers for engine torque, bike & rider weight,
and calculate the approximate lifting force generated by the tension in the
chain. We will ignore some other
forces acting during acceleration so we can focus on chain tension and the
associated lifting forces. This is
not completely accurate, but close enough to make the point of this analysis.
Sketch Explanations: Straight
lines with arrows indicate forces and their direction of application.
Circular lines indicate torque with the arrow showing the direction of
application. The numbers indicate
magnitude. To understand the
effects of a force (straight arrows) drawn at some angle other than vertical or
horizontal, we “resolve” the angled force into its horizontal and vertical
components. In our example, ‘X’
will indicate horizontal and ‘Y’ will indicate vertical forces.
All forces must balance at some force equilibrium condition.
When we twist the throttle, the tension in the chain is added to the
force equilibrium analysis. This
added force causes a new equilibrium condition and a short-term vertical
acceleration (rear end lift) to get to this point!
CHAIN TENSION
CALCULATIONS AND HOW THEY AFFECT THE FRAME
We will assume a total weight of 400 lbs for bike and rider.
We will look at suspension reactions with all the weight shifted to the
rear wheel modeling maximum acceleration. We
will place the rear swing arm in the horizontal position to keep things simple.
First we must approximate the tension in the chain. To accelerate, the engine produces torque at the drive sprocket; which applies tension to the chain; which then drives the rear sprocket. We will choose a 250cc engine that produces about 25 ft/lbs of torque. The second gear ratio is about 2 to 1 and the primary reduction ratio is about 2.5 to 1. Total engine torque multiplication in second gear equals 5 to 1; thus drive sprocket torque is 125 ft/lbs (25x5=125). For any torque, the force exerted is dependent on the leverage arm length. In our example the front sprocket diameter is 3.5”. The radius is 1.75” or .145 ft. Dividing 125ft/lb of torque by the front sprocket radius of .145ft. yields approximately 850 lbs of potential chain tension (125/.145 = 850). Since the rear tire typically slips in second gear, it is apparent that tire traction cannot contain all the available engine torque. The engine starts to ‘free wheel’ at some point below its maximum torque potential, thus the tension in the chain doesn’t reach its full potential. Tire slippage is dependent on terrain and rider technique. A reasonable ‘SWAG’ (scientific wild ass guess) for actual chain tension in 700 lbs. We’ll use this number for our analysis.
Note Sketch ‘A’. In this sketch we first see a diagram of the two sprockets with a chain drawn between them. Note the actual rise (vertical component) is 3.25”.
Note Sketch ‘B’. The second diagram resolves the chain angle into X and Y components (distances) so we can calculate the angle of the chain. The angle calculates to 8 degrees thus the 700 lbs of chain tension is at an 8-degree angle with respect to the horizontal swing arm.
Note Sketch ‘C’. To determine the effects of 700 lbs of chain tension at the rear wheel and at the frame, we must resolve the chain tension into its perpendicular components with respects to the swing arm. Note from our example that the horizontal force ‘Fx’ calculates to 693 lbs. The vertical force ‘Fy’ calculates to 100 lbs.
Note Sketch ‘D’. This
sketch shows the forces acting on the rear wheel and the frame that hold the
system in equilibrium. First note
the horizontal force labeled Fx at the rear wheel.
It is held in equilibrium by an equal and opposite Fx1 force exerted by
the frame at the front swing arm pivot. These
two forces cancel each other and combine to compress the swing arm some
negligible amount. The vertical
forces are much more interesting. The
Fy force acts at the rear wheel and its associated equilibrium force Fy1 is
applied at the frame. In the
standard ‘rigid body’ analysis, Fy1 and Fy would combine to form a
‘couple’, or torque, which would exert a torque or twisting force on the
entire bike. However in our case, the swing arm is attached with bearings
at both ends, so our two vertical forces are separated by a pivoting link
system. This link allows the two
opposite vertical forces to cause vertical displacement instead of a torque.
The rear wheel Fy tries to make the swing arm go down in the rear.
The ground prevents this motion. The
opposite vertical force at the front sprocket Fy1 tends to lift the frame, which
unloads the rear shock spring. By
applying 100 lbs of lifting force directly to the frame, the rear spring is
relieved of 100 of the total 400 lbs of rider and bike weight. This causes the bike to rise.
Out on the track, when the throttle is applied quickly, chain tension
occurs instantly causing the bike to lift as if the rider had suddenly lost 100
lbs. This sudden loss of a
100-pound load from the rear spring causes the bike to accelerate upward to its
new equilibrium point.
DISCUSSION AND
APPLICATION
Remember, we chose 400 lbs for the total bike weight and we said all the
weight would be transferred to the rear wheel during acceleration. Without chain tension forces, all 400 lbs is transferred to
the rear wheel through the rear shock spring.
When we consider the chain tension and analyze the resulting vertical
forces at the rear wheel and frame, we realize that 100 of the 400 lbs of bike
weight is applied directly to the rear wheel via the tension in the chain.
The remaining 300 lbs are supported by the rear shock spring.
The advantage of the conventional chain layout is the rider’s ability
to use this upwards force to his advantage for pre-jumping obstacles and
clearing double jumps. As discussed
earlier, this 100 lbs upward force reduces the weight carried by the spring.
When you relieve the spring of part of its load, it accelerates upwards to a new equilibrium position. When
the rider coordinates this upward frame acceleration with a jump takeoff, the
result is more upward motion and more distance.
Chain tension also tends to reduce bottoming when landing from large
jumps. Landing with the throttle on
reduces suspension bottoming because the shock spring only has to support the
impact forces from 300 lbs rather than the 400 lbs combined weight of the bike
and rider. The remaining 100 lbs is
supported by the tension of the chain. Note
that the ‘Torque Eliminator’ system eliminates these forces so the rider
cannot ‘dial in’ frame lift or anti-bottoming with the throttle.
The disadvantage of the
traditional chain alignment is that 100 lbs of the bike weight is carried by the
“rigid” chain connection between the frame and rear wheel, thus the rear
wheel behaves as if it had 100 extra pounds of ‘unsprung’ weight during
acceleration. Any ‘unsprung’
weight has trouble following the changes in terrain.
Adding another 100 lbs to this ‘unsprung’ weight during acceleration
adversely affects the rear tire’s ability to follow the terrain.
(This adds another reason to exit a turn one gear higher.
The higher the gear, the less the engine torque is multiplies; thus, the
rigid connection between the frame and rear wheel is minimized!)
The ‘Torque Eliminator” product effectively eliminates the rigid
connection between the frame and rear wheel.
By aligning the chain parallel to the swing arm, the chain tension
becomes parallel to the swing arm. Without
an angle between the chain and the swing arm, the forces are purely horizontal
with no vertical components. No
vertical forces mean no frame lift and no rigid connection between the frame and
rear wheel. All 400 lbs of bike and
rider weight act as ‘sprung’ weight transmitted to the ground through the
rear shock spring. This also
explains why the ‘Torque
Eliminator’ product requires a stiffer shock spring. Without the 100 lbs vertical force at the frame to counter
rear end squat during acceleration, the bike requires a stiffer spring rate to
eliminate excessive squat. Most
riders experimenting with this ‘Torque Eliminator’ system found that they
preferred the potential for frame lift over a smoother ride.
It should be noted that a 500 cc bike has about 1.5 times more torque
than a 250 cc bike and proportionally greater chain tension. Conversely a 125 cc bike would have about half the potential
chain tension of a 250 cc bike. Additionally,
there is more engine torque multiplication / chain tension in the lower gears
and less in the higher gears. This
explains why reactions at the rear wheel and frame will be more noticeable in
the lower gears with large displacement bikes.
Happy trails and don’t forget to ‘Gas It’ to clear that next obstacle or double jump!