2. Design
Tire Selection
The tire we chose was the Hoosier 18.0 X 7.5-10 R25B with ITP 10 inch aluminum rim. We
chose 10 inch rim over 13 inch rims, because it has less rolling resistance. The disadvantage is
the risk of overheating the tire after a long periods of continuous use.
Suspension Geometry
The goal for this year’s suspension geometry is to maximize contact patch of the outside wheel.
As maximizing contact patch also maximizes traction that leads to increase in cornering load and
results in faster cornering speeds. A small degree of camber angle is designed in to the geometry
to compensate the camber gain during cornering.
The front suspension geometry is designed to have 1.8 degrees of negative camber at static. The
Camber gain rate is 0.745 degrees per degree of body roll. The maximum theoretical cornering
force in the front is 1.32g’s.
The rear suspension geometry is designed to have 1.04 degrees of negative camber at static. The
Camber gain rate is 0.47 degrees per degree of body roll. The maximum theoretical cornering
force in the rear is 1.25g’s.
AR-9: Savage has 50.8 percent of the weight in the front, with total weight of 536 lb w/o driver.
The following analysis is assumed to have a 150 lb driver and when the vehicle is taking a right
turn.
3. Static weight on
each tire w/
150lb Driver (lb)
Lateral Weight
Transfer (lb)
Weight on tire
during cornering
(lb)
Tire
Force/Traction
(lb)
LF 173.56 +97.63 271.19 ~360
RF 173.56 -97.63 75.93 ~95
LR 168.77 +94.56 263.33 ~340
RR 168.77 -94.56 74.21 ~90
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑊𝑊𝑊𝑊𝑊𝑊 𝑊𝑊ℎ𝑡𝑡 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 =
𝑊𝑊𝑊𝑊𝑊𝑊 𝑊𝑊ℎ𝑡𝑡 𝑜𝑜𝑜𝑜 𝑉𝑉𝑉𝑉ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∗ 𝐶𝐶𝐶𝐶 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿ℎ
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑊𝑊𝑊𝑊𝑊𝑊 𝑊𝑊ℎ𝑡𝑡 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 =
686𝑙𝑙𝑙𝑙 ∗ 13.7 𝑖𝑖𝑖𝑖
48.9 𝑖𝑖𝑖𝑖
= 𝟏𝟏𝟏𝟏𝟏𝟏. 𝟏𝟏𝟏𝟏 𝒍𝒍 𝒍𝒍
Front weight transfer = 192.19*0.508 = 97.63 lb
Rear weight transfer = 192.19*(1- 0.508) = 94.56 lb
Average Cornering Load = Traction/Total Weight of the vehicle = 885/686 = 1.29 g’s
Front Cornering Load = 455/343 = 1.32 g’s
Rear Cornering Load = 430/343 = 1.25 g’s
Rear cornering load is less than the front indicating that the vehicle will likely to over steer.
Front suspension spec:
4. Caster Angle: 7 degree (+/- 1 degree)
Scrub Radius: 1.643 inches
King Pin Inclination: 8.37 degree
Track: 48.923 inches
Camber w/ 150lb driver: 1.80 degree (negative)
Swing-Arm Length: 108.00 inches
Upper Control Arm Length: 10.65 inches
Lower Control Arm Length: 13.40 inches
Ride Height: 6 inches (Front)
Roll Center: 0.943 inches (above ground)
Max. CG height: 14.123 inches
Rear suspension spec:
Caster Angle: 1 degree
Scrub Radius: 2 inches
King Pin Inclination: 0 degree
Track: 49.95 inches
Camber w/ 150lb driver: 1.04 degree (negative)
Swing-Arm Length: 46.95 inches
Upper Control Arm Length: 9.55 inches
Lower Control Arm Length: 12.5 inches
Ride Height: 4.26 inches (Front)
Roll Center: 1.39 inches (above ground)
Max CG Heights: 14.420 inches
5. Center of Gravity
The vertical CG is found through the tilt test where the front of the vehicle is tilted upward to a
certain height, then we used scales to measure the weight difference between the front and rear,
as shown in the diagram below. It is important to keep the vertical CG as low as possible to
avoid excessive weight transfer.
𝐷𝐷𝑐𝑐𝑐𝑐ℎ =
𝐷𝐷𝑐𝑐𝑐𝑐𝑐𝑐 ∗ 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤
𝐷𝐷𝑢𝑢𝑢𝑢
+
((𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ∗ 𝑊𝑊𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) ∗ 𝐷𝐷𝑤𝑤𝑤𝑤)
(𝐷𝐷𝑢𝑢𝑢𝑢 ∗ �𝑊𝑊𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 + 𝑊𝑊𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟�)
+ 𝐷𝐷𝑤𝑤𝑤𝑤
Once the weight difference has been determined, we used excel to find the vertical CG.
The vertical CG is determined to be 13.7 inches off the ground, which is 0.4 inches below the
maximum vertical CG. The moment arm is 12.8 inches (front) and 12.3 inches (rear) which is
found by subtracting vertical CG with roll center distance. The distance between roll center and
vertical CG should be as low as possible, as the length of the moment arm determines the amount
roll during cornering.
6. Rocker
The initial constrains were the wheels need to have a travel range of 2 inches, 1 inch up and 1
inch down. The shock we have chosen (Tanner Vision) has a travel range of 3.18 inches, which
means the ideal shock to wheel motion ratio is 1.59. However, that is unlikely because we also
have to consider situations when the wheels travel more than 2 inches. So the actual motion ratio
should be lower than 1.59.
The rocker motion ratio for the front is designed to be 1.565 and the rear is 1.72. However, the
effectiveness of the rocker depends on the location of the push rod. In the front the rocker is 83%
effective, so the front wheel to shock motion ratio is 1.29. In the rear the rocker is 54% effective,
so the rear wheel to shock motion ratio is 0.92. The result shows that the rear has less mechanical
advantage than the front which means the rear require higher spring rate.
7. Spring Selection
One major factor of spring selection is the length of the moment arm. The length of the moment
arm relates to roll angle. Greater the length creates a larger the moment, which mean a stiffer
spring is needed to counter the moment. However, too stiff of a spring means that the wheel
cannot follow the ground, which ultimately leads to loss of traction. So a right balance of spring
stiffness is important.
The spring supplier did not provide us with the spring rate thus we are relying on the following
equation to find out the spring rate.
𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 𝐒𝐒𝐒𝐒 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 =
𝐆𝐆𝐝𝐝𝟒𝟒
𝟖𝟖𝟖𝟖𝐃𝐃𝟑𝟑
G = Torsional modules for steel = 11.25 x 10^6
d = Wire diameter in inches
N = Number of active coils
D = Mean coil diameter in inches
8 = Constant for all coil springs
The design body roll is 2 degrees, as it gives the best outside wheel chamber. To achieve 2
degrees of body roll, the wheels need to travel in jounce 0.84 inches in the front and 0.86 inches
in the rear, and the force the spring needs to resist is 5532.5 lbf-in. From the wheel rate
calculation the best spring rate for the front is 168.25lb/in and for the rear is 333.8 lb/in.
The springs we chose are Tanner Hot Spring #140 in the front with rate of 272.84 lb/in and #185
in the rear with rate of 336.5 lb/in.
8. Wheel Rate
Wheel rate is determined form spring rate and the suspension geometry.
𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 = 𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 𝐒𝐒𝐒𝐒 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 �
𝐚𝐚
𝐛𝐛
(𝑴𝑴𝑴𝑴𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓𝒓)�
𝟐𝟐
𝐱𝐱 �
𝐜𝐜
𝐝𝐝
�
𝟐𝟐
Variable a, b, c, and d can be determine from the 2-D suspension geometry.
𝐅𝐅𝐅𝐅𝐅𝐅𝐅𝐅𝐅𝐅 𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 = �𝟐𝟐𝟐𝟐𝟐𝟐. 𝟖𝟖𝟖𝟖
𝒍𝒍 𝒍𝒍𝒍𝒍
𝒊𝒊 𝒊𝒊
� �
𝟏𝟏𝟏𝟏. 𝟑𝟑𝟑𝟑"
𝟏𝟏𝟏𝟏. 𝟓𝟓𝟓𝟓"
(𝟏𝟏. 𝟓𝟓𝟓𝟓𝟓𝟓)�
𝟐𝟐
𝐱𝐱 �
𝟏𝟏𝟏𝟏𝟏𝟏. 𝟒𝟒𝟒𝟒"
𝟏𝟏𝟏𝟏𝟏𝟏. 𝟎𝟎𝟎𝟎"
�
𝟐𝟐
= 𝟒𝟒𝟒𝟒𝟒𝟒. 𝟔𝟔𝟔𝟔
𝒍𝒍 𝒍𝒍𝒍𝒍
𝒊𝒊 𝒊𝒊
Front wheel rate = 432.69 lb/in
𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖𝐖 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 = �𝟑𝟑𝟑𝟑𝟑𝟑. 𝟖𝟖
𝒍𝒍 𝒍𝒍𝒍𝒍
𝒊𝒊 𝒊𝒊
� �
𝟓𝟓. 𝟒𝟒𝟒𝟒"
𝟏𝟏𝟏𝟏. 𝟎𝟎𝟎𝟎"
(𝟎𝟎. 𝟗𝟗𝟗𝟗)�
𝟐𝟐
𝐱𝐱 �
𝟒𝟒𝟒𝟒. 𝟖𝟖𝟖𝟖"
𝟒𝟒𝟒𝟒. 𝟗𝟗𝟗𝟗"
�
𝟐𝟐
= 𝟐𝟐𝟐𝟐𝟐𝟐. 𝟏𝟏𝟏𝟏
𝒍𝒍 𝒍𝒍𝒍𝒍
𝒊𝒊 𝒊𝒊
Rear wheel rate = 260.14 lb/in
Damper Selection
Damper is determined from the spring rate and sprung mass. The goal of the damper is to damp
out excessive spring motion. Critical damping is desired as it is just soft enough to prevent spring
oscillation, yet not too hard so wheels can still follow the road.
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐 = 2√𝑚𝑚𝑚𝑚
𝜑𝜑 =
𝐶𝐶
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐
𝜑𝜑 = damping ratio
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐 = Critical damping
Based on the selected spring the front critical damping is 20.6 lb*s/in and rear is 22.52 lb*s/in
9. NOTE: the equations only work for SI units, the result (kg/s) needs to be converted back to
English unit (slug/s). However slug/sec equals to lb*s/ft to get the final answer we need to divide
the result by 12 to get lb*s/in
The Tanner Vision shock data can be found in the following graph:
Form the graph it shows that the Vision shocks highest damping(C) is approximately 15.6 lb*s/in
for both jounce and rebound.
Front: For both jounce and rebound the damping ratio is 76% at 0.8 in/sec
Rear: For both jounce and rebound the damping ratio is 69% at 0.8 in/sec
The chosen shocks in slightly underdamped, which means the vehicle will experience a small
oscillation during a bump.
10. Components
Once the key suspension points have been determined, we use Solidworks to design the shape of
the control arm, upright, and hub to match the given spec.
Fully Assemble Front Suspension
Fully Assemble Rear Suspension
11. Validation
To make sure the parts do not fail during operation, we use Solidworks FEA simulation to
validate the strength of each part. We first calculate the load on each component then use the
values for the FEA simulation.
Load Calculation (Cornering)
The following free body diagram and equations represent the loading forces on each component
during cornering. However, it does not represent the actual suspension geometry.
+→ � 𝑭𝑭𝒙𝒙 = 𝟏𝟏. 𝟐𝟐𝟐𝟐𝒎𝒎𝒎𝒎 + 𝑭𝑭𝑼𝑼𝑼𝑼𝑼𝑼 𝒄𝒄𝒄𝒄𝒄𝒄 𝜶𝜶 − 𝑭𝑭𝑷𝑷𝑷𝑷 𝒄𝒄𝒄𝒄𝒄𝒄 𝜷𝜷 − 𝑭𝑭𝑳𝑳𝑳𝑳𝑳𝑳 𝒄𝒄𝒄𝒄𝒄𝒄 𝜽𝜽
+↑ � 𝑭𝑭𝒚𝒚 = 𝒎𝒎𝒎𝒎 − 𝑭𝑭𝑼𝑼𝑼𝑼𝑼𝑼 𝒔𝒔𝒔𝒔𝒔𝒔 𝜶𝜶 − 𝑭𝑭𝑷𝑷𝑷𝑷 𝒔𝒔𝒊𝒊 𝒊𝒊 𝜷𝜷 − 𝑭𝑭𝑳𝑳𝑳𝑳𝑳𝑳 𝒔𝒔𝒔𝒔𝒔𝒔 𝜽𝜽
+� � 𝑴𝑴𝑨𝑨 = 𝟏𝟏. 𝟐𝟐𝟐𝟐𝒎𝒎𝒎𝒎𝒎𝒎 − 𝒎𝒎𝒎𝒎𝒎𝒎 − 𝑭𝑭𝑼𝑼𝑼𝑼𝑼𝑼 𝒄𝒄𝒄𝒄𝒄𝒄 (𝜶𝜶)𝒂𝒂 − 𝑭𝑭𝑷𝑷𝑷𝑷 𝒔𝒔𝒔𝒔𝒔𝒔 (𝜷𝜷)𝒅𝒅 + 𝑭𝑭𝑷𝑷𝑷𝑷 𝒄𝒄𝒄𝒄𝒄𝒄 (𝜷𝜷)𝒆𝒆
Where mg is 171.5lb, 1.25 is maximum theoretical cornering force in G’s. The angles and
distance of each distances was found using the 2-D geometry.
From the calculation the load on the upper control arm is 142.68 lbf, lower control arm is 220.10
lbf and push rod is 227.98 lbf.
12. Load Calculation (Braking)
For braking calculation we are assuming the vehicle is traveling at 30 mph and come to a full
stop in 3 seconds.
𝑭𝑭 =
𝑴𝑴 ∗ ∆𝑽𝑽
∆𝒕𝒕
𝝉𝝉 = 𝒓𝒓 ∗ 𝑭𝑭
𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳 𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾 𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻 =
𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 ∗ 𝑪𝑪𝑪𝑪 𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉𝒉
𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩
M = 686lb, ∆𝑽𝑽 = 30mph = 44ft/s, ∆𝒕𝒕 = 3 sec
𝒓𝒓 = 3.5 inch
𝑭𝑭 =
𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 ∗ 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒/𝒔𝒔
𝟑𝟑𝟑𝟑
= 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏. 𝟑𝟑𝟑𝟑 𝒍𝒍 𝒍𝒍𝒍𝒍
𝝉𝝉 = 𝟑𝟑. 𝟓𝟓
𝒊𝒊 𝒊𝒊
𝟏𝟏𝟏𝟏
∗ 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏. 𝟑𝟑𝟑𝟑 𝒍𝒍 𝒍𝒍𝒍𝒍 = 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐. 𝟓𝟓𝟓𝟓 𝒇𝒇𝒇𝒇 ∗ 𝒍𝒍 𝒍𝒍𝒍𝒍
𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳 𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾 𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻 =
𝟔𝟔𝟔𝟔𝟔𝟔 𝒍𝒍 𝒍𝒍 ∗ 𝟏𝟏𝟏𝟏. 𝟕𝟕 𝒊𝒊 𝒊𝒊
𝟔𝟔𝟔𝟔 𝒊𝒊 𝒊𝒊
= 𝟏𝟏𝟏𝟏𝟏𝟏. 𝟔𝟔𝟔𝟔 𝒍𝒍 𝒍𝒍
13. The total braking force is 10061.33 lbf, but since there are total of 8 control arms the load on
each control arm is actually 1257.67 lbf. While the torque exerted on the suspension is 2934.55
ft*lbf, but since there are 4 suspension systems the load on each system is actually 733.63 ft*lbf.
In addition the longitudinal weight transfer is 156.64 lb in the front so each front wheel exerted
78.32 lbf.
Finite Element Analysis (FEA)
We use Solidworks simulation for the FEA analysis. The beam members are treated as solid
instead of shell to have a more accurate result. We apply 733.63 lbf tangents to the control arm to
simulate braking load combines with 220.10 lbf normal to the control arm to simulate cornering
load and 78.32 lbf weight transfer load. The fixture was applied at the opposite end of the control
arm.
From the simulation we conclude that in order to achieve Factor of Safety of 2 the control arm
needs to have the minimum wall thickness of 0.06 inch, using AISI 4130 high carbon steel.
14. Fabrication
The fabrication consisted of hand profiling, MIG welding and machining. Due to low budget
issue most of the fabrication was done in-house. The summary of the suspension cost analysis is
shown below:
The total cost of the entire suspension system is $2051.17 with total material cost of $1804.09
and total labor cost of $236.65
The control arms are made out of 4130 steel 5/8 inch round tubing with a wall thickness of 0.06
inches, combined with high strength 5/16 rod ends from McMaster for the pivot points and weld
nuts. A wooden jig was created so we can MIG weld the components together. The space insert
was made out of 6061-T6 aluminum, since it was cheap to purchase and easy to cut. The bushing
is made out of delrin solid rod, we then used a manual lathe to form the desired shape.
15. Front upright is made out of 1018 steel with square and rectangle tubings, and the front spindle is
also made out of 1018 steel with 1.5 inch solid rod, a section of the rod was machine down to 1
inch using a lathe. The spindle and the upright components were welded together to form the
uprights. The rear upright is made out of 7076-T6 aluminum and we used a CNC mill to form the
shape.
16. The front hub started out as a 6061-T6 7 x 3 inch aluminum rod, then it was shaped by using a
lathe. The rear hub was purchased from Taylor Race. The bearing we chose for the hub is
Timken taper bearing with an ID of 1 inch slip fit with tolerance of -0.002 inch. Eight M10 studs
were used in the front hub for the wheel mounting lugs. We used two aluminum adaptor plate for
the rear wheel mount.
17. Testing
We ran mainly two types of tests, skid pad and brake test. Skid pad test determines the actual G
force the vehicle is capable of achieving. While the Brake test validates the strength of the
suspension components.
Skid Pad
The actual G load the vehicle can take can be found using the following equation
𝐆𝐆 =
𝟏𝟏. 𝟐𝟐𝟐𝟐𝟐𝟐 𝐱𝐱 𝐑𝐑
𝐓𝐓𝟐𝟐
R = Radius of the turn in feet
T = Time in second require to complete a turn
The theoretical time for the vehicle to go over a 30 feet radius skid pad is 5.42 seconds. On the
actual test we got about 5.7 as fastest time indicating the actual maximum G force as 1.13g’s.
The reason could be the tire wasn’t hot enough or the geometry was off. More tests are needed to
confirm the result.
18. Brake Test
The result of the brake test shows that the rod ends do not have sufficient strength when we
locked the wheels at 30 mph. The rod ends sheared off causing the front upright to disconnect
from the control arm. From this experience we determined that rods in bending are not an
appropriate design for suspension. We quickly re-designed the control arm where the ball joint
acts as the pivot point of the control arm, removing rods in bending.
The picture above shows the aftermath of the brake test with insufficient strength in the rod ends.
Too much load was applied at the rod ends and sheared the head off.
The picture above the shows the re-designed control arms. Ball joints replaced the rod ends
which decrease the moment at the pivot points.
