Motorcycle Rotation
COPYRIGHT © 2015 GEORGIA PUBLIC SAFETY TRAINING CENTER
www.gpstc.org
MOTORCYCLEROTATION
COPYRIGHT © 2013 GEORGIA PUBLIC SAFETY TRAINING CENTER www.gpstc.org Terminal Performance Objective
Familiarize students with a method of calculating the impact speed of a motorcycle in a motorcycle vs car collision, when the impact causes the other vehicle to rotate.
Enabling Objectives
• Introduce the concept of angular (rotational) velocity and
define terms and units.
• Discuss the concept of torque acting on the vehicle through
the tire/roadway interface during vehicle rotation.
• Introduce a formula to calculate rotational velocity of a
vehicle once its torque is known.
• Discuss the relationship between the rotation of the vehicle after impact, and the delta‐V experienced by the motorcycle during impact.
• Use the motorcycle’s delta‐V to calculate its impact speed.
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Advanced Reconstruction with CDR
www.cdr‐trainers.com
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Angular Velocity
• BMW laying drags video
• The BMW has very little linear motion but a lot of rotation.
• Note that the BMW is not rotating about its center of mass,
but about its front axle. We’ll see this again later.
Rotational terms and units
• Rotational terms and equations are similar to the linear terms and equations we are already familiar with:
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Distance
Velocity
Acceleration
Mass
Force
Momentum
Energy
Rotational terms and units
Linear
d = distance (ft)
v = velocity (ft/sec)
a = accel. (ft/sec/sec)
Angular
θ [theta] = displacement (radians)
ω [omega] = velocity (rad/sec)
α [alpha] = accel. (rad/sec/sec) One radian is the angle formed by laying one radius on the circumference of a circle.
180⁰ = 3.14 radians (π)
360⁰ = 2π radians
Degrees ÷ 57.29 = radians
180⁰ ÷ 57.29 = 3.14 radians
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Rotational terms and units
Mass Moment of Inertia
An object’s resistance to angular (rotational) acceleration.
Linear
m = mass
(resistance to linear accel.)
Angular
I = mass moment of inertia
(resistance to angular accel.)
Video… Science of Golf: Torque and Moment of Inertia
Rotational terms and units
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An object’s mass moment of inertia is dependent upon:
The mass of the object
The shape of the object
The axis of rotation (it’s easier to spin an object about its center of mass than about another point of rotation)
Rotational terms and units
Mass moment of inertia for vehicles
• Vehicles have complex shapes and varying densities
• Calculating their true I‐values is nearly impossible
• A vehicle has three axes of rotation (yaw, pitch, roll); each axis has its own moment of inertia
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Rotational terms and units
• Experimental value databases exist for different vehicles
• Google “NHTSA Inertia Database”
• REC‐TEC software also contains I‐values for vehicles
• Simple equations can approximate I‐values
Rotational terms and units
Mass moment of inertia regression equations:
(Garrott et. al., “Vehicle inertial parameters – measured values and approximations,” SAE Technical Paper no. 881767, 1988.)
Cars:
Iyaw = 1.03w – 1206
Ipitch = 0.99w – 1149
Iroll = 0.18w – 150
Light trucks:
Iyaw = 1.03w – 1343
Ipitch = 1.12w – 1657 Iroll = 0.22w – 235 These equations result in approximate values for I. They are not valid for mid‐engine cars. The vehicle weight w is entered in pounds and the resulting units are lb‐ft‐sec2
Other concepts
Some equations require the vehicle’s mass (instead of weight).
The Imperial unit for mass is the slug.
Mass = w ÷ g
3500 lbs ÷ 32.2 ft/sec2 = 108.7 slugs
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Other concepts
Moment arm (L): The length of the lever. The longer the lever, the easier it is to move an object. The farther the point of impact is from the point of rotation, the longer the moment arm.
PDOF is determined by the investigator. The moment arm (L) is measured in feet from the point of rotation to the PDOF line, at a 900
angle to the PDOF line.
Here the car is rotating about the front axle, so Ladj is the distance from the front axle to the PDOF line. Information Required for Analysis
Target Vehicle:
WB wheelbase (ft)
Wa weight on axle closest to damage (lbs)
θ
total vehicle rotation angle (radians) – impact to rest
M1 mass of vehicle (slugs)
I
yaw moment of inertia of vehicle
Dcom distance from the farthest axle (rotation point) to vehicle center of mass (ft)
L length of moment arm (PDOF to center of axle of rotation) (ft)
Motorcycle:
Mm V4 Φ
Ψ
mass of motorcycle (slugs)
post impact speed of motorcycle (ft/sec)
departure angle of motorcycle (degrees)
approach angle of motorcycle (degrees)
Roadway f
Torque – Exercise #1
• First step in the rotational analysis
• If the impact is non‐central, the struck end of the vehicle moves while the opposite axle acts as a pivot • As the vehicle rotates, torque acts between the tires and
roadway to slow the rotation to a stop
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Rotational Velocity – Exercise #2
• Use the torque calculated in Exercise #1 to calculate the rotational velocity of the vehicle caused by the impact
Rotational Velocity – Exercise #3
• Use the car’s rotational velocity calculated in Exercise #2 to
calculate the motorcycle’s change in velocity.
Rotational Velocity – Exercise #4
• Use the motorcycle’s change in velocity calculated in Exercise #3, along with the motorcycle’s post‐impact (departure) speed to calculate the motorcycle’s impact speed.
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Use the same process to work the Windy Hill Road motorcycle vs. Kia collision.
– Kia yaw moment of inertia
– Torque acting on Kia between road and tires
– Rotational velocity of Kia
– Motorcycle Δv
– Motorcycle impact speed
– Combined speed using pre‐crash evidence
Review of Objective
Familiarize students with a method of calculating the impact speed of a motorcycle in a motorcycle vs car collision, when the impact causes the other vehicle to rotate.
Questions?
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