The following is my Rule26 report based on a crash incident that took place at a family ranch
when two sisters were driving a 2015 Polaris RZR XP 1000. The analysis and calculation done on the
report is heavily based on the evidence and measurements given in the report and also primarily, on my
education as a Mechanical Engineer. Also, calculations are done based on equations from the book
Fundamentals of Traffic Crash Reconstruction by John Daily, Nathan Shigemura and Jeremy Daily. I
reserve the right to edit this report if new, useful evidence becomes available.
Description of Accident
Two cousins, Susanne and Claire, were riding on a new 2015 Polaris RZR XP 1000 at a family
ranch. The UTV had an aftermath lift kit correctly installed by Claire’s dad who was a master mechanic.
They had set up a course which involved using a berm as a jump. Susanne, the younger cousin was
driving the UTV of off a berm which had a takeoff angle of 5 degrees. After landing, they tried to take a
left turn and under the circumstances, the Polaris rolled over. Susanne, the driver said she was wearing
the seatbelt and her helmet and hence suffered no injuries. Claire however was sprawled on the ground
with her helmet 10 feet away from her. She suffered a broken back and hence was paralyzed from the
waist down. Susanne also claims she heard a loud bang, like something broke while she was turning
after the jump. Upon further inspection, it was found that the upper control arm of the right rear
suspension arm was separated and there was dirt logged in the rim of the right front wheel. A more
detailed summary and information can be found in the measurements table.
I have been given the assignment to give an opinion on the speed of the UTV going off the jump,
the speed of the UTV just before the rollover, tipping angle in its original as well as lifted configuration, if
the stock UTV would have rolled over in this scenario and finally give an opinion on the root cause of the
A complete statement of opinions the witness will express and the basis and reasons for
*Note: In doing a crash analysis, there are bound to be discrepancies due to a variety of factors. To fully
reconstruct what exactly happened on a crash site is impossible which would lead to uncertainties in
values. Also, while measuring for these values, the equipment’s itself will have some uncertainty. I will
try and incorporate these uncertainties while solving for my values.
1) The speed of the UTV going off the jump was calculated to be approximately 49.1 miles per hour
using the equation derived on page 494 from the Fundamentals of Traffic Crash Reconstruction. The
equation is 𝑆𝑜 =
. In the above equation, ‘So’ is the required velocity off the jump, ‘d’ is the
horizontal distance, ‘h’ is vertical distance of the center of mass and θ being the angle of the ramp which
in this case is the berm.
2) Before getting into the calculation for the speed of the UTV before rollover, it is important to know
the velocity of the UTV while it was turning as it can give us an insight into what actually caused the
crash. But, to know the speed when it was turning is quite challenging due to the lack of sufficient data
such as the distance travelled by the UTV after the jump or physical evidence measurements collected at
the crash site. I will get into the assumptions and calculations for this speed later on. This is where the
field indicators sketches come in. From the attached exhibit, the critical speed yaw scuff marks have
been provided. Ch 13: Critical Speed Yaw from Fundamentals of Traffic Crash Reconstruction from Dr.
Daily’s book has some handy equations which help solve for these values. Equation 13.1 from the book
states that 𝑆 = 3.86√𝑓𝑟 where ‘S’ is the Critical Speed yaw in mph, ‘f’ is the drag factor and ‘r’ is the
radius of the center of mass path in feet’s. From the report we were given a range of 0.65-0.74 for the
coefficient of friction. Radius of the center of mass path was calculated by equation 13.3 from Dr. Daily’s
book. The equation is 𝑟 =
where r’’ is the required radius, ‘c’ is the chord measurement and
‘m’ is the middle ordinate measurement. In the report ‘c’ was given to be 30 feet and ‘m’ was given to
be 0.48 feet which in turn gave a value of roughly 235 feet for ‘r'. Finally, plugging in the value of ‘r’ and
the range values for the friction factor in the equation to calculate Critical speed yaw gives a range of
values from 53.4 to 60.7 miles per hour. These values and the equations used would be further
discussed in the succeeding parts.
3) This section deals with the tip over angles for the UTV in its original as well as lifted configuration.
Firstly, it is important to know when does a tip over happens. A tip over will take place when the center
of mass of the object under consideration lies outside the last point of contact. In the given case, the
UTV will tip over if its center of mass lies outside the last point of contact which is the Normal force
exerted by the tires upwards. The angles can be found using basic geometry. A picture is shown below
to show various steps used in calculating for the angles.
UTV modeled as inclined to help solve for θ.
In the above figure, θ = 2 − β = 90 − β. From the above geometry, 𝑡𝑎𝑛𝛽 =
= 𝑡𝑤 . Now, solving
for β gives β = 𝑡𝑎𝑛−1 (𝑡𝑤). Finally, now incorporating θ gives two equations for the two values of the
angles necessary. In the UTV’s original configuration, θ = 90 − 𝑡𝑎𝑛−1 (𝑡𝑤) where ‘h’ is the center of
mass height in the original configuration which in this case is 2 feet and ‘tw’ is the track width which in
this case is 4.33 feet. Solving for θ approximately gives 47.3°. Now again, solving for θ for the lifted
configuration is done by θ = 90 − 𝑡𝑎𝑛−1 [(𝑡𝑤+𝑡𝑤𝑎𝑑𝑑 )] where h+hadd = 2.83 feet and tw+twadd= 4.75 feet.
The difference in the values is because of the center of mass height and track width increased in the
lifted configuration. Solving for θ in the lifted configuration gives approximately 40°. The values of the
two angles makes sense as when we consider the height increase from the lifted configuration, the tilt
of the vehicle is more deeper which accounts for a lesser value for θ.
4) This section deals whether the broken suspension lead to the crash. Equation 20.1 from page 708 of
Dr. Daily’s book is useful in determining whether the UTV tipped over because of the broken suspension.
The equation 𝑓 = 2ℎ 𝑐𝑜𝑠𝑒 + 𝑠𝑖𝑛𝑒 is used to calculate the propensity to roll. ‘tw’ is the track width, and
‘e’ is the super elevation angle. Given in the report, ‘e’ was said to be -3%. By using trigonometric
function, ‘e’ in terms of angle was found to be -1.72°. Plugging the required values in the propensity
equation gives f to be 0.817 in the UTV’s lifted configuration which basically means that it would require
0.817 grams to make the UTV tip. For our given values of µ between 0.65-0.74, if we consider Figure 1,
where the UTV is at an incline and is about to tip over, there would be a force applied upwards due to
the friction in the tires. In our case, even if we consider the maximum value of 0.74 for the coefficient of
friction, it would mean it needs 0.74 grams to tip over which is still less than 0.817 calculated above.
Now, calculating the propensity to roll over in the original stock configuration gives a value of f = 1.052.
As in the lifted case, same theory is applied to the stock UTV in its original state. 0.74 grams is still less
than the 1.052 grams. Therefore, from the above calculations and discussion, it is fair to say that the
broken suspension was indeed responsible for the crash and not any external forces like speed.
5) Finally, this section deals with the root cause of the crash. To make the discussion easier, I have added
a schematic at the end of this section. The initial velocity was found to be approximately 49.1 miles per
hour. But for a moment, let us consider the velocity of the UTV when it was making the turn after jump.
This is not to be confused with the speed just before the rollover. To do the calculations, a few
equations come in handy. Let us treat the vehicle as a rigid body, so when it is making the turn,
𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛= ma . Now, further saying that 𝑎 =
where ‘a’ is the centrifugal acceleration. Now, replacing
‘a’ in the Friction equation and letting that equal to ‘µmg’, we get to the final equation thus solving for
𝑉 = √𝜇𝑅𝑔 where µ is the coefficient of friction between 0.65-0.74, ‘R’ is the calculated radius of
gyration which came out to be 235 feet and g is 32.2 feet/s2. We get a range of values for the velocity at
the curve due to the coefficient of friction ranges given in the report. Solving for’ V’, we get the range to
be between 47.8-51.3 miles per hour which keep in mind is less than the velocity range just before
tipping over calculated in Section 2 to be between 53.4-60.7 miles per hour. Of course, the calculations
done to find the velocity at the curve are a near approximate as it is impossible to know the exact
velocity. The result was obtained by making assumptions and substituting values. But, nevertheless it
does give us an insight into speed most near to. Considering, the range of values for the speed at the
curve, are smaller than the range of values for speed calculated just before tipping over tells me that
speed was not a factor based on the accident. All the above calculations and assumptions and opinions
bring me to the final conclusion that it is the manufacturers fault in the UTV being tipping over.
A schematic showing UTV’s various speeds at different location.
Purchase answer to see full attachment