Σ⁶

 Fundamentals of Vehicle Dynamics – A Primer For Improving Lap Times

​

An SAE Lecture

University of British Columbia – Vancouver, BC, Canada

October 22, 2025

SAE Disclaimert

Σ⁶

Speaker content not managed by SAE and may reference competition

operations, rules, etc. However, they are not an authority operating body;

content may conflict with event rules, operations, etc.

SAE Disclaimer

SAE Disclaimert

Σ⁶

Agenda

ASX Presentation Agenda

1. Steady State Forces Acting On An Automobile
1. Aerodynamic Forces
2. Tire Forces

​

• Suspension Design
• Understanding Tire Characteristics
• Front Suspension Fundamentals
• Rear Suspension Fundamentals

​

• Powertrain Overview
• ICE
• Electric
1. Hub Motor Impact on Handling

​

• Lightweight Design Principles

​

​

Σ⁶

Part 1.: Steady State Forces Acting on a Vehicle

1. Steady State Forces Acting on An Automobile

Aerodynamic Force

Tire Reaction Force

Aerodynamic Force = p x FT_A x C_d x V²; p = Air density, FT_A = Frontal area, C_d = Coefficient of Drag, V = Velocity;

Tire reaction Force = T_c x W_v T_c = Tire coefficient of rolling resistance, W_v = Vehicle weight

Total Force = Aerodynamic Force + Tire Reaction Force

Total Power Required: (Aerodynamic Force + Tire Reaction Force) x Vehicle Speed

Vehicle Weight

Σ⁶

Part 1.1.: Aerodynamic Forces

1.1. Aerodynamic Forces Acting on An Automobile

Height

Width

Frontal Area (FT_A) = Width x Height x Shape Factor*

​

*Shape factor is the effective % of a rectangle actually

occupied by the vehicle; it is always less than 1.

Example: if a vehicle is 4’high and 6’ wide the total area

in the rectangle is 24 ft²; if the vehicle occupies 20 ft₂

the Shape Factor is 20/24 or 83.3% - Note that the tires

are part of the vehicle frontal area

​

Units

F_AS = Slugs ((lb–ft)/second²)

F_AF = Lbs

p = Lbs./ft³

FT_A = Ft²

C_d = dimensionless

V = Ft/Second

Aerodynamic force is an exponential function, e.g., the aero force at 70 MPH is about double the aero force at 50 MPH

(70 MPH x 70 MPH = 4900, 50 MPH x 50 MPH = 2500, 4900/2500 = 1.96 )

https://x-engineer.org/aerodynamic-drag/

Aero Drag Force Is 4x Higher at 200 kph

Than It Is At 100 kph: 800 N vs. 200 N

1.1. Shape vs. Drag – NASA Study

https://physics.stackexchange.com/questions/201633/what-shape-has-the-highest-drag-coefficient

4.3x Reduction

6.6x Reduction

Flat Plate To Airfoil

Drag Reduction: 28.4x

​

1.1. Options to Consider That Reduce Aerodynamic Forces

1. Lower Vehicle
2. Reduce vehicle width
3. Minimize mirror area, integrate into body or eliminate (replace with digital rear view camera)
4. Minimize tire width, i.e., reduce Shape Factor
5. Reduce underbody turbulence, e.g., add a flat belly pan
6. Minimize external heat exchanger opening area
7. Utilize NACA ducts (low drag submerged air inlets) for heat exchanger airflow
8. Add aero aids to minimize engine compartment turbulence
9. Reduce grille opening actively at speed, e.g., speed sensitive shutters that close at higher velocities
10. Reduce C_d, i.e., minimize body turbulence by minimizing/eliminating right angles
11. Add aero features to driver’s helmet so it is tuned to the vehicle airflow
12. Use teardrop or bullet shapes for all hardware in the airflow stream, e.g., oval tubing for front suspension links

Σ⁶

Part 1.2.: Tire Forces

1.2. Tire Forces Acting on An Automobile

https://autos.yahoo.com/news/lotus-evora-400-convertible-confirmed-070000248.html

T_RF = T_c x W_v

T_c = Rolling resistance coefficient

W_v = Vehicle weight

Tire force is linear and is proportional to vehicle weight and tire rolling resistance coefficient

Units

​

T_RF = lbs.

T_c = dimensionless

W_v = lbs.

​

​

Tire Force Equation

Vehicle Weight

Tire Reaction Force

1.2. Basic Tire Physics

https://x-engineer.org/rolling-resistance/

Flat Road Rolling Resistance

Where f is the rolling resistance coefficient

1.2. Tire Rolling Resistance Coefficients

Low Rolling Resistance (LRR) Class

0.0062 to 0.0103 Range

1.2. Tire RRC vs. Velocity

https://x-engineer.org/rolling-resistance/

S Rated Tire: 112 MPH; H Rated Tire: 130 MPH; V Rated Tire: 150 MPH

Typical FSAE Max Speed

1.2. Sliding Tire Friction Coefficients

https://automotivepapers.wordpress.com/2023/02/13/tire-friction-overview/#:~:text=For%20tires%20the%20main%20friction,friction%20coefficient%20around%201.30%2D1.35.

-When a tire starts sliding, e.g., locked up in braking, it becomes a block of rubber in shear

acting against the road surface

- The sliding friction coefficient drops off as sliding speeds increase

1.2.: 275 mm Width Racing Slick Weight vs. Diameter

Size Tread Width Weight Delta

​

275/35ZR15 10.1” 21 lbs. Base

​

275/45ZR16 10.3” 24 lbs. +3 lbs., +0.2”

​

275/35ZR17 10.1” 23 lbs. +2 lbs., 0.0”

​

275/35ZR18 10.3” 23 lbs. +2 lbs., 0.2”

​

https://www.tirerack.com/tires/tires.jsp?tireMake=Hoosier&tireModel=R7&sidewall=Blackwall%20(Mount%20DOT%20inside)&partnum=735ZR8R7&tab=Sizes

Hoosier R7 Racing Slick

Increasing This Tire Diameter Increases Unsprung Weight About 10%

While Increasing Tire Contact Width by 2% Or Less

1.2. Tire Inertia vs. Tire Diameter

Tire Size R1 R2² R1² + R2² % Change

​

275/35ZR15 15.0” 12.0” 369 in² Base

​

275/35ZR17 17.0” 14.0” 485 in² +31%

​

​

1. https://pressbooks.bccampus.ca/physics0312chooge/chapter/10-3-dynamics-of-rotational-motion-rotational-inertia/#:~:text=The%20moment%20of%20inertiaI%20of%20an%20object%20is%20the,I%3D%20∑%20mr2.

A Larger Tire Diameter Increases Tire Inertia Non-Linearly: A 13%

Diameter Increase Raises The Tire Inertia By 31%

2. https://hpwizard.com/rotational-inertia.html

Wheel Inertia Calculation¹

g_r – gear ratio

r_t – tire dynamic radius

m_e – non-rotating tire mass equivalent

m – static tire mass

I – tire inertia

​

Inertia Impact on Effective Tire Mass²

3. 3.0” sidewall height used for both calculations

1.2.: Options to Consider To Minimize Tire/Wheel Weight

1. Optimize/minimize tire width to reduce weight
2. Optimize/minimize wheel width to reduce weight
3. Determine tire coefficient of friction for best all-around performance
4. Determine minimum wheel diameter that allows required brake rotor diameter and use that diameter
5. Investigate composite wheels to reduce weight

Σ⁶

Part 2: Suspension Basics

Σ⁶

Part 2.1.: Understanding Tire Characteristics

2.1.. Vehicle Steer Modes

​

1. Neutral Steer: Front and rear tires have the same slip angles: four wheel drift,

no steering input required to maintain cornering radius

​

1. Understeer: Front tire slip angle > rear tire slip angle; requires steering into the turn

to maintain cornering radius

​

3. Oversteer: Rear tire slip angle > front tire slip angle; requires added steering away

from the turn to maintain cornering radius and to prevent a spin

​

https://racingcardynamics.com/understeer-and-oversteer/

Oversteering Formula Car

2.1. Tire Slip Angles vs. Lateral Force:

The Key To Maximizing Lateral g’s

https://suspensionsecrets.co.uk/tyre-slip-angle/

10 SA

Loss of Lateral Force at 10 degree Slip Angle

High performance tire vs. standard performance tire

– 50% more lateral force at

the same slip angle

2.1. Suspension Objectives

Physics 101: A vehicle will generate maximum cornering acceleration (g’s) when the traction of all

four tires is 100% utilized, i.e., all four tires are on the ground in the “Ideal” position

​

Suspension Design 101: The objective of a suspension is to maximize the tire contact patch and optimize the slip angle

during high lateral g cornering while minimizing tire wear

​

https://www.linkedin.com/posts/garrett-adams-55566a247_bmwmotorsport-fasttrackracing-activity-6960631582239981568-SFZZ?trk=public_profile_share_view

Inside Front Tire In a High “g” LH Turn

Tire Is Off The Ground

2.1. Tire Force Vector Diagram

TE_N - Maximum Tractive Effort Force

A

C

TE_L- Maximum Lateral Force

B

Tire Peak Force A = B = C;

Calculate Combined TE_N + TE_L Forces Using Rt. Angle Triangle Formula

​

​

​

C: 80% x 80% = 0.64; 60% x 60% = 0.36; 0.64 + 0.36 = 1.0; ⎷1.0 = 1.0

80% TE_N

60% TE_L

- At A there is 0 Lateral Force Available

- At B there is 0 Tractive Effort Force Available

- C Combines Tractive Effort and Lateral Force Tire Force Components

C Uses 80% of Peak TE and 60% of Peak Lateral Force

0

2.1. Neutral, Understeer and Oversteer Examples

https://www.pinterest.com/pin/247909154463812252/

https://farausa.com/cars-for-sale/

https://nasaspeed.news/columns/driver-instruction/weight-watching-understanding-weight-transfer-and-racecar-dynamics/

Neutral Steer

Understeer

Neutral Steer

Hang On and Hope Steer

Inside Front Tire Is On The Ground

Inside Front Tire Is Off

The Ground

2.1. Cornering Capability Basic Physics

​

Pick a Tire To Meet Peak Cornering Loads

Parameters

Cornering Acceleration: 1.5 g’s

Car Weight: 3500 lbs.

Total Peak Lateral Force: 3500 lbs. x 1.5 = 5250 lbs.

​

Tire A: 4 x 899 = 3596 lbs. < 5250 lbs.

​

Tire B: 4 x 1349 = 5396 lbs.> 5250

If SA > 6 degrees this tire won’t develop the

required cornering force

Tire B: 3 x 1349 lbs. = 4047 lbs. < 5250 lbs.

​

Tire C: 4 x 1799 lbs. = 7169 lbs. > 5250 lbs.

Tire C: 3 x 1799 lbs. = 5397 lbs. > 5250 lbs.

If SA > 7 degrees this tire won’t develop the

required cornering force with 3 tires

​

​

C - 1799 lbs.

B - 1349 lbs.

A - 899 lbs.

SA = Slip Angle

2.1. Tire Pressure vs. Tire Contact Patch Area

15 PSI Contact Patch

Tire Plan View

Tire Plan View

25 PSI Contact Patch

Normal Tire Load With

175 lb. driver and 475 lb. car:

650 lbs./4 = 162.5 lbs./tire

​

Tire contact patch area:

T_A15 = N_L/P_T

T_A15 = 162.5 lbs./15 lbs./in²

T_A15 = 10.83 in²

​

​

Tire contact patch area:

T_A20 = N_l/P_T

T_A20 = 162.5 lbs./20 lbs./in²

T_A20 = 8.13 in²

​

​

​

​

Tire contact patch area:

T_A25 = N_l/P_T

T_A25 = 162.5 lbs./25 lbs./in²

T_A25 = 6.50 in²

​

http://farnorthracing.com/autocross_secrets12.html

Grip is proportional to tire pressure*

*For this curve – excessive tire pressure will

begin to decrease grip as the sidewall distends

and the contact patch shrinks

20 PSI Contact Patch

Tire Plan View

2.1. Tire Contact Patch vs. Tire Pressure

https://www.hankooktire.com/us/en/help-support/care-guide/tire-pressure.html

Wheel Low

Wheel High

Normal Wheel Height

2.1. Tire Pressure Tuning Tips

​

Run the car on as many surfaces as possible and record this

information in your chassis Log Book with all chassis settings*

G_L (Lateral g’s) = (V²/R)/1 g

- V = Velocity in ft/second

- R = skid pad radius

- 1 g = 32.2 ft/second²

​

Example

V = 62.8 ft/second;

R = 100 ft.

G_L = (62.8 x 62.8/100)/32.2

G_L = 1.23 g’s

Calculate Average Velocity on 200’ Diameter Skidpad

- Distance = 2 pi R = 6.2832 x 100’ = 628 ft.

- Time/lap: 10.00 seconds

- V = 628 ft/10.00 seconds = 62.8 ft/second

Skid Pad Calculations

Author’s Notes:

I prefer to use an average skid pad lateral g number

by timing each lap and using the formulas at the right.

If you don’t have an accelerometer, you can download an

app to your phone or make one by putting colored water

in a clear bottle and calibrating it. A 45 degree angle is

0.707 g’s, i.e., engine sump oil is at a 45 degree angle at

0.707 g’s. Use an iPhone to video the vertical & secure

bottle for each lap. Record all tire temperatures immediately

after each lap across the entire tread area.

​

*Ambient temperature & humidity, tires, wheels, toe,

camber, castor, ride height, springs, corner weights, etc.

http://farnorthracing.com/autocross_secrets12.html

Σ⁶

Part 2:2. Front Suspension Fundamentals

2.2. Why Use An Independent Suspension?

https://gomechanic.in/blog/car-suspension-types-india/

- Independent suspensions decouple the LH and RH tires

- Tire input forces are not transferred from side to side during impacts

- Improves vehicle control by maximizing tire contact patches

2.2. Front Suspension Components - RWD

​

1. Tires

​

• Front Suspension – Rear Drive Vehicle
1. Upper control arms
2. Lower control arms
3. Springs
4. Shock Absorbers
5. Stabilizer bar
6. Bushings/Heim joints

​

​

​

​

​

​

Coil Spring SLA

(Short/Long Arm)

Torsion Bar SLA

MacPherson Strut

Transverse Leaf Spring SLA

(Short/Long Arm)

https://www.motortrend.com/features/how-it-works-september-1993-982-1506-64-1/?galleryimageid=e6240361-7b11-462e-8b99-37b5c6c43835

https://www.corvettesalvage.com/product/c5-used-front-suspension-assembly-1997-2004/

2.2. Key Front Suspension Component Functions - RWD

3. Springs – Resist vertical loads

* Coil (steel)

* Leaf Spring – Longitudinal (steel) – 4WD Trucks

* Leaf Spring – Transverse (fiberglass) – Corvettes

* Torsion bar (steel) Old Chrysler Corporation cars

* Air Spring

* Hydraulic Spring

​

4. Shock absorbers – control springs from resonating at suspension natural frequencies

* Gas filled

* MagnetoRheological (MR - electromagnetically variable fluid viscosity)

​

5. Stabilizer bars – transfer cornering forces from inside tire to outside tire

- Front suspension: larger bar diameter increases understeer

- Rear suspension: larger bar diameter reduces understeer/increases oversteer

* Solid (steel)

* Hollow (steel)

​

​

​

​

MR Shock Operation

2.2. SLA Instant Center and Roll Axis Determination

- Instant Center (IC) is set up by the intersection of the UCA and LCA angles – IC length increases as UCA angle

moves towards parallel with bottom control arm

- UCA inboard pivot point is lower than outboard pivot point to create best camber curve relative to a

horizontal LCA

- Longer IC decreases camber gain with suspension travel

- Roll center is intersection of IC line with vehicle centerline

- Ideal front suspension roll center height is 2” to 4” above the ground

Intersection of RH tire IC and vertical

centerline of tire contact patch

LCA

UCA

Outboard UCA

Pivot Point

2.2. SLA Instant Center and Roll Axis Determination Details

Instant Center

– RH Tire

1. Extend lower control arm line

2. Extend upper control arm until it intersects the lower control arm line

3. The intersection of these two imaginary lines is the instant center of rotation for the tire

4. Draw a line from the instant center to the centerline of the tire contact patch

5. Draw a vertical line at the vehicle front view centerline

6. The intersection of line 4. with line 5. is the suspension roll center

2.2. SLA Front Suspension Overview

Nominal Ride Height

Ride Height at 40 mm Jounce (compression)

- Roll center is significantly lower than nominal

ride height

Roll Axis Changes with Suspension Travel

Instant Center

– RH Tire

Instant Center

– LH Tire

The ideal front roll center height is 2” – 4” above the ground for most vehicles*

*https://motoiq.com/the-ultimate-guide-to-suspension-and-handling-its-all-in-the-geometry-part-one-the-roll-center/3/

2.2. Camber Angle vs. Wheel Travel

​

Target: Minimize camber change throughout full range of suspension travel

https://www.researchgate.net/figure/Camber-angle-VS-Wheel-travel_fig4_319629129

Full Jounce

(Spring Compression)

Full Rebound

(Spring Extension)

Instant Center

Instant Center

Kingpin

2.2. Inboard IC vs. Outboard IC

Correct UCA Angle: Inboard UCA pivot is lower than outboard

UCA pivot (for horizontal LCA) and IC is inboard of tire

Vehicle Centerline

Vehicle Centerline

Incorrect UCA Angle: Inboard UC pivot is higher than outboard

UCA pivot (for horizontal LCA) and IC is outboard of tire

Instant Center – Front SLA Suspension

(Theoretical Intersection)

​

2.2.: Inboard IC Tire Contact Patch vs. Outboard Tire Contact Patch

The objective of a suspension is to maintain a normal tire contact patch as the body rolls

Outboard IC

Inboard IC: Contact patch is maximized

with body roll

Outboard IC: Reduces contact patch with body roll

Max Lateral g RH Turn

CCW Body Roll, CCW Tire Rotation in Jounce

CCW Body Roll, CCW Tire Rotation in Rebound

CCW Body Roll, CW Tire Rotation in Jounce

CCW Body Roll, CW Tire Rotation in Rebound

Inboard IC

https://www.carsized.com/en/cars/lotus-evora-2015-coupe/front/

SLA Front Suspension vs. MacPherson Strut

- An SLA Design Allows A Substantially Longer Swing Arm Than a MacPherson Strut Design

- A Longer Swing Arm Reduces Camber Change vs. a MacPherson Strut And Maintains A

Larger Tire Contact Patch

- Given Sufficient Packaging Room An SLA Suspension Enables Superior Tire Control (Porsche GT3:

“With the double wishbone, we have a way to make the car stiffer and more stable with less body movements under braking. But we could gain some residual comfort for street use. So even though it’s twice as stiff compared to the front axle on the last GT3, it’s no less useable as a road car – and still perfectly useable for a GT3 Touring.”¹)

​

https://www.google.com/url?sa=i&url=https%3A%2F%2Fm.facebook.com%2Ffanpageengineerspost%2Fphotos%2Fa.102694554976066%2F568543168391200%2F&psig=AOvVaw2tKTXen2Mb8F-X2x_1nXdB&ust=1708379883753000&source=images&cd=vfe&opi=89978449&ved=0CBEQjRxqFwoTCKDy0ZPxtYQDFQAAAAAdAAAAABAF

The swing arm length for a MacPherson strut is the distance from the lower control arm pivot point to the tire centerline (shown by red arrow)

Strut Swing

Arm Length

Camber Change

1. https://www.topgear.com/car-news/supercars/time-geek-out-new-porsche-911-gt3s-suspension

Σ⁶

Part 2.3.: Rear Suspension Fundamentals

2.3. Rear Suspension Components - RWD

​

1. Tires

​

• Rear Suspension – Rear Drive Vehicle
1. Upper control arms
2. Lower control arms
3. Springs
4. Shock Absorbers
5. Stabilizer bar
6. Bushings/Heim joints
7. Longitudinal links
8. Lateral links

​

​

​

Four Link Live Axle

(Truck and Drag Racer Usage)

https://www.rcnmag.com/tech/suspension-guide

https://silodrome.com/citroen-2cv-history/

Citroen 2CV Rear (& Front) Suspension

https://medium.com/roadster-life/2cv-charleston-when-6-months-turned-into-10-years-8710e889780a

2.3. Key Rear Suspension Component Functions - RWD

3. Springs – Resist vertical loads

* Coil (steel)

* Leaf Spring – Longitudinal (steel) – Trucks

* Leaf Spring – Transverse (fiberglass) – Corvettes

* Air springs

* Hydraulic springs

​

4. Shock absorbers – control springs from resonating at suspension natural frequencies

* Gas filled

* MagnetoRheological (MR - electromagnetically variable fluid viscosity)

​

5. Stabilizer bars – transfer cornering forces from inside tire to outside tire

- Front suspension: larger bar diameter increases understeer

- Rear suspension: larger bar diameter reduces understeer/increases oversteer

* Solid(steel)

* Hollow (steel)

​

​

​

​

MR Shock Operation

2.3. Roll Axis vs. Center of Gravity – Bikes

https://www.researchgate.net/figure/Adjustable-position-of-the-roll-axis-and-yaw-axis-When-changing-the-ratio-K-between-the_fig18_258176893

CG

Roll Axis

Center of Gravity

LH Turn – Torque reaction is CCW

Lateral Acceleration Vector

Roll Axis

Motorcycles and Bikes Lean Into Turns Because Their CG Is Below The Roll Axis

2.3. Swing Axle – Simple and Inexpensive IRS

https://www.theautopian.com/our-suspension-engineer-explains-why-this-one-suspension-design-parameter-has-such-a-huge-effect-on-ride-handling-and-body-roll/

https://driventowrite.com/2016/03/21/theme-suspension-swinging-on-a-star/

MB 300 SEL Race Car Used Swing Axles

https://motoiq.com/the-ultimate-guide-to-suspension-and-handling-its-all-in-the-geometry-part-one-the-roll-center/3/

2.3. Corvair Swing Axle - 1964 vs. 1965

https://www.theautopian.com/our-suspension-engineer-explains-why-this-one-suspension-design-parameter-has-such-a-huge-effect-on-ride-handling-and-body-roll/

https://www.corvairforum.com/forum/viewtopic.php?t=13284

Corvette style double

CV joint added to 1965

Corvair halfshafts to

eliminate wheel jacking

1963 Corvette IRS

1965 Corvair IRS

1963 Corvette IRS and 1965 Corvair

IRS are conceptually very similar

2.3. Rear Suspension IRS Designs

Mercedes Benz IRS

Corvette C8 IRS

https://www.corvetteforum.com/forums/c8-general-discussion/4190068-c8-suspension-geometry.html

Porsche IRS

Jaguar IRS

Rear Suspension Swing Arm Length Determination

The Sideview Intersection of a Four Link Rear Suspension is the Intersection of the Upper and Lower Control

Arm Extensions

The Sideview Intersection of a Two Link Rear Suspension With One Control Arm Per Side (Jaguar IRS on

previous slide) Is The Distance From the Tire Centerline To The Link Pivot Point in A Side View

Pivot Point

Front of Car

Front of Car

Correct UCA Angle: Forward UCA pivot is lower than Rear

UCA pivot and IC is towards front of vehicle

Swing Arm Length

Swing Arm Length

Swing Arm Length

2.3. Independent Rear Suspension Design Basics

Key Differences Between Front and Rear Independent Suspensions

- Differential integrated into suspension

​

- Differential mounted to body structure

and serves to limit halfshaft lateral movement

​

- Lateral links resist TE torque

​

- Lateral links control toe

​

- Fore-aft control links determine swing arm length which resists wheel hop (acceleration)

​

- Propshaft adds fore-aft control

​

- Higher roll center: Target 4” to 10” vs. 2” to 4” for front roll center

https://www.google.com/search?client=safari&rls=en&q=IRS+Suspension+drawing&ie=UTF-8&oe=UTF-8#imgrc=34zDvPMW1RU7MM&imgdii=_7ABxLV4UGkaZM&ip=1

https://motoiq.com/the-ultimate-guide-to-suspension-and-handling-its-all-in-the-geometry-part-one-the-roll-center/3/

Wheel Hop Equation (F_L > W_T)

​

F_L = T_E/X

F_L = Tire Lifting Force

T_E = Engine Torque x Gear Ratio

X = Swing Arm Length

W_T = Vehicle Weight on One Tire

F_L

X

IC

T_E (CW)

W_T

Rear Suspension Camber Control

Identical To The Front IRS Calculations

Vehicle Centerline

Roll Steer Model - Roll Understeer Is Target

Front Roll Center Height: 4” Rear Roll Center Height: 10”

Y_F = Front Torque Arm Length; Y_R = Rear Torque Arm Length

https://motoiq.com/the-ultimate-guide-to-suspension-and-handling-its-all-in-the-geometry-part-one-the-roll-center/3/

1. Y_F arm length > Y_R arm length;

2. Therefore torque acting on front suspension is > torque acting

on rear suspension;

3. This torque loads the front outside tire more than the rear

outside tire in a turn

4. The result is understeer (roll understeer at the cornering limit is

generally desirable)

You lose less time correcting for understeer than you do correcting for oversteer

4” RC

10” RC

Front

Rear

Σ⁶

Part 3.: Powertrain Overview

3. ICE vs. Electric Motor Output Characteristics

ICE - NA

Electric Motor

https://www.carthrottle.com/news/how-do-electric-vehicles-produce-instant-torque

https://www.researchgate.net/figure/Power-and-torque-demand-curve-in-electric-vehicles_fig2_320611871

3. ICE - NA Power Delivery

(Naturally Aspirated)

ICE - NA

ICE – NA Characteristics

​

1. Gradual torque build-up

2. Low torque at low RPM

3. Narrow peak torque RPM range

4. Narrow peak power RPM range

5. Much lower efficiency than an electric motor

https://www.carthrottle.com/news/how-do-electric-vehicles-produce-instant-torque

HP = (Torque x RPM)/5252

3. ICE – Turbo Power Delivery

ICE - Turbo

ICE – Turbo Characteristics

​

1. Earlier peak torque than NA ICE

2. Turbo peak torque is flat over a broad RPM range

3. Broad peak power RPM range vs NA ICE

4. Higher specific output than NA engine

5. Much lower efficiency than an electric motor

https://twitter.com/GregKable/status/725993061008990208

3. ICE – BSFC (Brake Specific Fuel Consumption)

Typical Units

​

- Lbs./HP-hr

- Lbs./kW-hr

- grams/HP-hr

- grams/kW-hr

​

- BSFC is a measure of fuel burning engine operating efficiency at discrete MAP-RPM points

- It is an empirical means of comparing changes in engine efficiency

- It is straightforward to measure on an engine dyno

BSFC Islands – Part Throttle

https://www.eng-tips.com/viewthread.cfm?qid=363722

BSFC Calculation

​

Dyno Run Time: 5 minutes

Dyno HP: 10.0

Fuel used: 100 grams

​

BSFC = Fuel/(Hp*Time)

BSFC = 100 grams/(10HP*1/12 hr.)

BSFC = 100 grams/0.83 Hp-hr

BSFC = 121 grams/HP-hr

Electric Motor

Electric Motor Characteristics

​

1. Peak torque at 0 RPM
2. Flat torque curve at low RPM
3. Rapid torque drop-off as RPM increases
4. HP linear as RPM increases past torque peak
5. Very high efficiency

​

​

3. Electric Motor Power Delivery

https://www.researchgate.net/figure/Power-and-torque-demand-curve-in-electric-vehicles_fig2_320611871

Tesla PM Motor

(Permanent Magnet)

3. Electric Motor Architecture Efficiency Comparison

https://insideevs.com/photos/683100/insideevs-us-single-photo-upload/#4082402_tesla-motor-efficiency-slides

Tesla Induction Motor

- 94% - 96% Peak Efficiency

- Large peak efficiency island

- 92% - 94% Peak Efficiency

- Much smaller peak efficiency island than PM motor

3. ICE vs. EV Vehicle Efficiency

Typical Electric Vehicle Efficiencies vs. ICE Counterparts

https://www.fueleconomy.gov/feg/byfuel/EV2023.shtml

Compact SUV: BEV is 3.8x More Efficient Than ICE

Electric Pick-up: BEV is 3.4x More Efficient Than ICE

General BEV Efficiency Improvement vs. ICE MPG : 3x to 4x

Comparable Size GM ICE Vehicle (Highest MPG variant)

MSRP Range : $25,900 to $30,500)

MSRP: $28,795

3. Electric Motor Powertrain Options – Part 1.

1. One electric motor driving two wheels through a differential
1. Allows ICE drivetrain hardware to be utilized
2. Minimum development for differential, LSD, and gearing
3. Moderate tuning effort for torque modulation
1. Uncertain which side tire will lose traction
1. Potential for drivetrain software to be conservative & overcompensate
1. Reduced power under the time curve could increase lap times

2. Two hub motors driving two wheels
1. Location Options
1. Two rear wheel hub motors
2. Two front wheel hub motors
3. One front mounted motor, one rear mounted motor
1. Same side mounting
2. Diagonal mounting
2. Torque vectoring capability tunable for specific tracks
• Aggressive for tight tracks/slalom rums
• Moderate for longer tracks
3. Maximized traction using software
• Tune for track/tire coefficients (mu)
4. Tunable regenerative braking
• RH/LH motors independently tunable

3. Electric Motor Powertrain Options – Part 2.

3. Four hub motors driving four wheels

• Four tire torque vectoring capability tunable for specific tracks
1. Aggressive for tight tracks/slalom rums
2. Moderate for longer tracks
• Maximized traction using software
• Tune for track/tire coefficients (mu)
• Maximum regen capability

​

3. Hub Motor Impact on Vehicle Dynamics

Lotus Engineering Hub Motor study¹ (Protean released study in public domain) concludes:

​

1. Normal chassis tuning processes (springs. shocks, bushings, etc.) can typically offset any

handling degradation caused by increased unsprung mass

​

2. Individual wheel motor control shows good potential for substantial improvements in

vehicle behavior

1. https://www.proteanelectric.com/f/2018/04/protean-Services3.pdf

• 2007 Ford Focus 1.6 “Style”

​

• Well damped European hatchback

​

• Unsprung mass addition of 30 Kg per corner

The Test Vehicle

1. https://www.proteanelectric.com/f/2018/04/protean-Services3.pdf

3. Hub Motor Impact on Vehicle Dynamics

The Test Vehicle

3. Hub Motor Impact on Vehicle Handling

1. https://www.proteanelectric.com/f/2018/04/protean-Services3.pdf

• Improved on-centre response gain characteristics with ST suspension bring straight ahead tracking stability back to reference level.

3. Hub Motor Impact on Steering Response

1. https://www.proteanelectric.com/f/2018/04/protean-Services3.pdf

• Steering feel and steering response characteristics with additional unsprung mass tend back towards reference when ST suspension is fitted.
• Steering kickback is reduced to reference level with ST suspension.

3. Lotus Subjective Assessment Results Summary

67

• Steering items were the most degraded by adding unsprung mass

​

• Stiffer suspension improved steering items to within ½ VER point of the reference

​

• Handling and agility was degraded with extra mass but not degraded further by stiffer suspension and on-centre tracking stability improved back to the reference.

​

• Some ride comfort items deteriorated slightly by fitting the stiffer suspension but this was not optimised for ride comfort. High frequency isolation was improved.

​

• The deficiencies resulting from increasing the unsprung mass could be largely counteracted by parts included in a typical R&H suspension tuning programme.

.

1. https://www.proteanelectric.com/f/2018/04/protean-Services3.pdf

Σ⁶

Part 4.: Lightweight Design Principles

“To add speed, add lightweight”

Colin Chapman, Lotus Founder

4. Building Blocks of Lightweight Design

​

• Design Principles

b. Lightweight materials don’t automatically create

a lightweight design

​

​

​

There are designs using lower density materials that are

heavier than similar designs using higher density materials

Lamborghini Aventador

Shelby GT500

4. Building Blocks of Lightweight Design

​

​

​

​

• The Lamborghini Aventador has a carbon fiber center tub with aluminum

front and rear substructures and is 200 lbs. heavier than the larger 2013

Mustang GT500 which has an all steel uni-body

​

• The Mustang specific density (lb./ft3) is 13% lighter than the Aventador:

12.2 lbs./ft³ vs 14.0 lbs./ft³

​

Measured Data from Car and Driver Magazine

1 L x W x H; Shape Factors: 0.75 - Aventador; 0.70 – Shelby GT500

​

​

​

https://www.dkfindout.com/us/animals-and-nature/birds/inside-falcon/

http://www.blog.illustraciencia.info/2019/10/skeleton-of-peregrine-falcon-katrina.html

4. Building Blocks of Lightweight Design

a. Design Principles

- 90 Degree joints are the enemy of lightweight design

- 90 Degree joints maximize torque loading and require

stiffer (heavier) structures to resist the higher torque

​

4. Building Blocks of Lightweight Design

​

a. Design Principles

c. Smooth load paths and transitions are key to a

lightweight design

​

​

​

​

C8 Corvette Chassis

https://jalopnik.com/heres-a-detailed-look-at-the-2020-corvette-c8s-impressi-1836540969

4. Building Blocks of Lightweight Design

​

a. Design Principles

d. Take advantage of exponential relationships

​

​

​

​

“Math is your friend”

I = bh³/Shape Factor

4. Building Blocks of Lightweight Design – Heavy Way

​

​

​

• Frame height constraint: 225mm; common width (55mm)

​

​

​

Note: Frames have no internal ribbing

Section Inertia Calculations

Deflection Calculations – Single Point Load

Input Data + Mass and Cost Calculations

Note: wall thickness iterated to equivalent deflection values

50% Tensile Strength Calculations

(Iterate to Solution)

4. Building Blocks of Lightweight Design – Heavy Way

​

a. Design Principles

d. Take advantage of exponential relationships

​

​

​

​

• Aluminum is 3x weaker than steel (tensile strength, Young’s modulus)

​

• In a constrained environment where the geometry is fixed this strength deficit cannot

be overcome

​

• The aluminum frame below (same H and W as the steel frame) is heavier than the

steel frame and is 75% more expensive (identical loads and deflections, peak stress

set at 50% of tensile strength )

​

​

​

4. Building Blocks of Lightweight Design – Light Way

​

​

​

• The key to a successful lightweight aluminum structure design is to maximize the section inertia by increasing the section height

​

• I = (BH³/SF) - (bh³/SF) where H(h) is the height, B(b) is the base and SF is the shape

factor, e.g., SF = 12 for a rectangle (H-h & B-b = wall thickness)

​

• Lotus Elise aluminum rocker height is 10” high vs. typical rocker height (steel) of 5”

​

• I value for 10” rocker ≈ 8x greater than a typical 5” steel rocker panel (no internal ribbing)

​

​

4. Building Blocks of Lightweight Design – Light Way

​

​

​

• No rocker height constraint: 250mm section height (Al) vs. 125mm (HSS)

​

Note: Frames have no internal ribbing

Section Inertia Calculations

Deflection Calculations – Single Point Load

Input Data + Mass and Cost Calculations

Note: wall thickness iterated to equivalent deflection values

50% Tensile Strength Calculations

(Iterate to Solution)

4. Building Blocks of Lightweight Design – Light Way

​

​

​

• No height constraint: 250mm section height used for aluminum design, 125mm

used for steel design – different frame widths and wall thicknesses

​

• Identical point loads at wheelbase mid-point, aluminum deflection (0.013mm) is ≈ ½ of the steel

rocker deflection (0.024mm), max stress = 50% of tensile strength for both materials

​

• Aluminum design is 40% lighter, less expensive and is significantly stiffer than the steel design

​

​

Note: Rocker panels have no internal ribbing

4. Building Blocks of Lightweight Design

​

a. Design Principles

e. Pay attention to the details

- Save a gram a day

- Track mass in 0.1 gram units (0.00022 lbs.)

​

​

​

Assumptions For Total Program Savings @ 1 gram/day

• 250 working days/yr.
• 2 year program
• 500 grams saved per student over the life of the program
• 25 students
• 12500 grams saved total
• 27.5 lbs. total weight savings

​

- Base weight: 475.5 lbs.; New weight: 448.0 lbs

- 5.8% total weight savings

4. Building Blocks of Lightweight Design

​

a. Design Principles

f. Use a total vehicle, holistic approach:

- Creates substantially lighter designs through mass

de-compounding affect

- Need approximately 20% mass reduction to drive

mass de-compounding:

- redesign BIW/chassis

- redesign closures

- redesign suspension

- reduce powertrain system weight

- Piece-mealing weight reductions, e.g., replacing

an aluminum floor pan with a carbon fiber floor

pan, doesn’t typically drive major weight savings

​

​

​

Σ⁶

The ASX Electric Vehicle

82

Cruise Efficiency (150 MPH): 18 MPGe

Cargo: Up to 2,000 lbs.

Noise: < 75 dBa @ 100’

Torque: > 6,000 lb. ft.

HP: > 1,000

Weight: < 4,000 lbs. with batteries

Range: 150 miles (2027 batteries)

> 700 miles (hybrid)

Top speed: > 240 MPH

Lateral g’s: > 3

Acceleration (g’s): .> 1

Landing site: 100’ diameter

https://www.iflyasx.com/about-us

Σ⁶

THANK YOU

Gregory E. Peterson

​

Gregg@asx.us