Suspension

Suspension Geometry

There are a number of different types of suspension geometries: live axel, swing axel, multi-link, double wishbone, MacPherson, etc. The most easily-adjustable suspension type is the multi-link geometry. It allows the highest amount of control over everything from kinematic roll center height to camber gain. The multi-link suspension for my car will have four main components:

  1. Upper Control Arm (UCA)
  2. Lower Control Arm (LCA)
  3. Upright
  4. Steering Link

The main variables in suspension geometry are:

  1. Upper and Lower Control Arm Vertical Angles – create the roll center height.
  2. Upright Fore-Aft Angle – creates the castor angle, which creates the mechanical trail distance.
  3. Upright Port-Starboard Angle – creates the kingpin inclination, which creates the scrub radius.
  4. Steering Link Vertical Angle – should intersect the instant center of the two control arms to avoid bump steer.
  5. Steering Link Horizontal Angle – creates the castor angle.
  6. Steering Link Length – should cause the pivot point axes to intersect at the rear tire, creating 100% Ackermann steering.

Coming up with these geometry dimensions requires setting limits and optimizing for specific design goals.

 

Track Width

Track width, often just called “track,” is the distance between the center of the tire contact patches for tires on the same axel. For 4-wheeled cars there is a front track and a rear track, for reverse three-wheelers, there is only a front track. All things being equal, a car with a wider track will have lower lateral weight transfer. Lower weight transfer results in improved traction, so obviously in order to improve performance we want to make the track width as wide as possible. A wider track also allows tires to load up more slowly as lateral weight transfers more slowly – this results in “smoother” handling. The trade off with having a wide track is it can make the vehicle hard to maneuver in narrow streets and in traffic. A wider track also adds weight unsprung weight to the vehicle. So the goal is to design the car with the widest possible track that still allows for easy maneuverability in traffic.

Here are track widths of some three-wheelers:

  • Aptera 2e: 1,953 mm
  • Elio 3-Wheeler: 1,697 mm
  • Morgan 3-Wheeler: 1,473 mm
  • Lotus Formula 1: 1,450 mm (front); 1,400 mm (rear)
  • Harley Trike: 1,397 mm
  • Bombardier Can Am Spyder: 1,308 mm

The maximum allowable vehicle width in the United States is 102 inches (2590.8 mm). The widest pickup truck available for sale is the the Dodge 3500 Dually, which is 96 inches (2,438 mm) wide. The track width on the Lotus Elise is 1,453 mm.

For my car I’m going to design it with a 1400 mm front track width.

 

Wheelbase-to-Track Ratio

The wheelbase is the distance between the tire contact patch of the front wheels and the tire contact patch of the rear wheel(s). The wheelbase-to-track ratio is the ratio between the the wheelbase length and the track width. Formula 1 cars must have a minimum wheelbase length of 3000mm and a maximum track width of 1800mm – giving them a minimum wheelbase-to-track ratio 0f 1.66:1. Coincidentally, this is almost exactly the golden ratio (1.618:1). The FIU FSAE team says that “for quick steering response an optimal ratio of 1.3 should be achieved.”

Based on my very rough estimates, I believe the Aprilia Magnet’s wheelbase is about 1700mm and its track is about 850mm – that is a wheelbase-to-track ratio of 2:1.

A 1.618:1 (golden ratio) wheelbase-to-track ratio with a 1400mm front track would put the wheelbase length at 2265mm.

 

Ride Height / Ground Clearance
The ride height is important because it helps determine the height of the vehicles center of gravity (CG). We want to keep our CG as low as possible, but lowering the ride height also lowers the amount of suspension travel that is possible, making it necessary to use harder springs, making the ride less comfortable. Lowering the ride height too much also risks bottoming out the car on bumps in the road. Thus, the ideal ride height is found by a compromise.

Here are some ride heights of various vehicles:

  • McLaren F1: 119mm
  • Ducati 848: 125mm
  • Harley Davidson Fat Boy: 130mm
  • Lotus Elise: 130mm
  • Ducati Monster: 150mm
  • Ferrari 355: 163mm
  • Ford Raptor: 241mm

I’m shooting for a ride height of  130mm.

 

Pushrod vs Pullrod
Instead of connecting the springs and dampers directly to the suspension arms, it is better to use pushrods or pullrods. Pushrods and pullrods reduce the unsprung mass of the car and improve the aerodynamics. Pullrods require the springs and dampers to be located low in the car, while pushrods require them to be located higher in the car. Since the motors and batteries will likely have a higher overall mass density than the springs and dampers, it makes more sense to use a pushrod suspension in order to keep the heavier components lower in the car, thereby lowering the center of gravity of the vehicle.

 

Bellcrank Geometry
The bellcrank is the component that connects the pushrod to the spring and damper. The bellcrank pivots around an axis in order to change the direction of force. Bellcranks can be designed with three different types of geometry: progressive, neutral or regressive. With a neutral bellcrank geometry, as the wheel moves up, the spring and damper are compressed the same amount. If the wheel moves 1 inch, the spring and damper are compressed 1 inch. If  the wheel moves two inches, the spring and damper compress by 2 inches. With a regressive bellcrank geometry, the spring and damper are only compressed at a fraction of the distance that the wheel moves, meaning the effective spring rate decreases as the suspension is compressed. So with a 0.5:1 regressive bellcrank geometry, a 2 inch wheel movement will only result in 1 inch of spring and damper compression. A progressive suspension geometry causes the spring and damper to compress at a multiple of the wheel movement, making the effective spring rate increase as the suspension is compressed. In a 2:1 progressive bellcrank geometry, a 2 inch wheel movement would result in a 4 inch spring and damper compression. The best design is a progressive bellcrank geometry. This is because under small wheel movements, the spring and damper don’t move much, but under large movements, the spring and damper provide increasing force.

A simple analysis of the Ariel Atom bellcrank shows that it has a 2.6:1 progressive bellcrank ratio:

ArielAtomBellcrank

I plan to have a simple 2:1 progressive bellcrank geometry on my car (meaning a 2 inch wheel movement would result in a 4 inch spring and damper compression).

 

Suspension Travel – bump/rebound mm
Suspension travel is important because it determines how large a bump the suspension can soak up. A car that is driven off-road needs a large suspension travel. A car that is driven on a smooth racetrack needs a smaller suspension travel. A road car needs a suspension travel somewhere in the middle.

Here are the suspension travels for some vehicles:

  • McLaren F1: 90 mm bump and droop front, 80 mm bump and droop rear
  • Lotus Elise: 50 mm droop / 60 mm bump front, 50 mm droop / 70 mm bump rear
  • 2004 Subaru WRX STI: 95 mm droop / 75 mm bump front, 100 mm droop / 100 mm bump rear
  • 2005 Subaru WRX STI: 95 mm droop / 65 mm bump front, 95 mm droop / 85 mm bump rear
  • Ducati 1199: 120 mm bump and droop front, 130mm bump and droop rear
  • Zero MMX Electric Motorcycle: 218 mm front, 227 mm rear
  • Baja 1000 Trophy Truck: 760+ mm

I’m planning to use three  Öhlins TTX36 in my suspension (the stock rear shock absorber for the Ducati 1198). This shock has a maximum stroke of 57mm. With a 2:1 progressive bellcrank geometry, the maximum bump/rebound of the car will be 28.5 mm.

If I wanted to make the car more 0ff-road capable (or simply better able to soak up big potholes) I could choose a shock absorber with a larger stroke, like the Öhlins TTX44 KT 994, which is used on the KTM 450 motorcycle. This shock has a 109mm stroke, which translates into a 54.5mm maximum suspension travel with a 2:1 bellcrank geometry.

 

Kinematic Roll Center Height (RCH)

The roll center is a theoretical point in space created by the intersection of two imaginary lines drawn from the instant centers of the suspension and the center of the tire contact patches. The roll center is the point about which the chassis rolls. By changing the angle of the suspension arms you can change the roll center and affect how the car will react to cornering forces. The the following diagram, the instant centers are represented by the blue dots while roll center height is represented by the yellow dot:

RollCenterHeight

The roll center height (RCH) is the vertical height of the roll center and is important insofar as it determines how the car will roll in a corner. The RCH must be designed in its relation to the center of gravity (CG) And to the ground plane. There are five possibilities:

  1. RCH above CG
  2. RCH=CG
  3. RCH below CG and above the ground
  4. RCH = ground level
  5. RCH below ground level

Here’s how each of the five possibilities plays out:

  1. RCH above CG: Bad. Putting the roll center height above the center of gravity height would actually cause the car to lean into corners – which sounds like it would be very desirable. However, putting the RCH above the CG also leads to extreme jacking forces, raising the sprung mass of the car. This can cause the car to flip over in a corner. Modern Formula 1 cars often have upward-sloping front a-arms that can cause the front roll center to be above the center of gravity. The purpose of this design is to create more aerodynamic downforce.  F1 teams offset this by having a normal suspension design in the rear, thereby creating a rearward-sloping roll axis. This likely causes modern F1 cars to understeer at low speeds.
  2. RCH=CG: Bad. All of the lateral force is transferred through the suspension arms and no force is transferred through the springs and dampers. The car will have no body roll, but the springs and dampers won’t be able to control anything.
  3. RCH below CG and above the ground: Good. The height as a percentage of the distance between the ground and the CG will determine what percentage of lateral forces will be transferred through the suspension arms and what percentage will be transferred through the springs and dampers. A higher roll center heights put more force through the suspension links and less force through the springs.
  4. RCH = ground level: Bad. All of the lateral force will be transferred through the springs and dampers and no lateral force will be transferred through the suspension arms. There would be no jacking or anti-jacking. The roll center will also migrate above and below the ground plane as the suspension moves, causing the forces acting through the suspension arms to suddenly change direction, making the car handle unpredictably. Parallel equal-length a-arms can create a situation where RCH = ground level.
  5. RCH below ground level: Bad. Creates extreme anti-jacking forces, lowering the sprung mass of the car, causing the car to squat in corners.

Higher roll center heights create less body roll but more jacking. Lower roll center heights create more body roll but less jacking. Since the car will be automatically tilted in towards the corner, we don’t need to worry about body roll and should instead focus on minimizing jacking forces. So for a tilting three-wheeler, the optimal RCH for this car is slightly above the ground but not too low that the RCH will fall below the ground plane as the car rolls in a corner.

The Lotus Elise has a kinematic roll center height of 30mm above the ground and a center of gravity height of 470mm. The Lotus Elise RCH is 6% the height of the CG, meaning 6% of lateral force is transferred through the suspension arms and 94% is transferred through the springs and dampers.

For this car I will aim for a front roll center 40 mm above the ground.

 

Static Camber Angle

Some camber angles of high-performance cars:

  • Ferrari F50: -0.7 degrees front, -1.0 degrees rear
  • Lotus Elise: -0.01 degrees front, -1.8 degrees rear
  • Ferrari 355: -0.5 to -0.8 degrees front, -1.8 to -2.0 degrees rear

I’m going to target a static camber angle of -2.0 degrees.

 

Scrub Radius

The scrub radius is the distance between the center of the tire contact patch and the point at which the kingpin axis intersects the ground. The scrub radius is thus determined by both the kingpin inclination and the width of the tire. The scrub radius provides driver feedback under braking by causing the steering wheel to pull towards the tire that is doing the most braking. Some driver feedback is good, but too much scrub radius can make the car difficult to handle under extreme braking. There are three possibilities for the scrub radius:

  1. Positive scrub radius – the kingpin axis intersection is on the inside side of the center of the tire contact patch. Almost all cars have a positive scrub radius. 
  2. Zero scrub radius – the kingpin axis intersects the center of the tire contact patch. Cars with zero scrub radius are described as “squirmy” because the scrub radius will actually move back and forth from positive to negative as forces change, causing the handling to become unpredictable.
  3. Negative scrub radius – the kingpin axis intersection is on the outer side of the center of the tire contact patch. The advantage of negative scrub radius is that in the event of a tire failure or brake failure on one wheel, the car will want to naturally steer itself in a straight line.

KPIandScrub

For performance cars with independent suspensions it seems to be generally accepted that the scrub radius should be positive and less than 1 inch (25.4mm). Some scrub radii of famous sports cars:

  • McLaren F1: 16.25 mm
  • Lotus Elise: 10.5 mm
  • Corvette C5: 10 mm
  • Mazda Miata: 0 mm

I am targeting a scrub radius of  15 mm.

 

Rod Ends

Rod ends are one of the most important and often most overlooked components of a car. Rod ends are spherical bearings build into threaded rod ends. They connect the suspension links to the uprights on one end and to the car’s hardpoints on the other end. The best rod ends are three-piece “self lubricating” units which use a Teflon liner instead of a grease bearing, making them nearly maintenance-free. Cheaper rod ends (called “economy” or “commercial” rod ends) are usually two-piece construction where the body is swaged around the bearing.

Key considerations when choosing a rod end are:

  1. Maximum force to be applied to the bearing – for example hitting a big pothole at 150 MPH – once multiplied by a safety factor of 3, this force should be below the operating load capacity of the rod end.
  2. Maximum misalignment angle – this is the angle when the suspension is at full compression or full release – a small amount of additional angle should be added to account for any flex in the suspension arms

I’m planning on buying from Aurora Bearing Company because they have a lot of good educational information on their website and because they provide 3D cad drawings of every part they sell.

For the front suspension I’m planning to use the same rod ends for all six points: Aurora Item # MM-M12T

For a comparison, McMaster-Carr sells a rod end with the same dimensions (#2988k151). The McMaster-Carr rod end has a static radial load capacity of 3,905 lbs of force. The Aurora rod end has a maximum static radial load capacity of 18,215 Newtons, which is approximately 4,094 lbs of force.

A very common design mistake is to put the rod end in bending.

 

Suspension Dimensions

Huw Davies has produced a nice visual suspension geometry calculator that allows you to play with these variables. My key model input parameters (in the “dimensions from vehicle” menu) are:

  • Chassis
    • Upper width: 320 mm (The tilting frame is 350 mm wide. The center of the rod end holes will be 15 mm from the sides)
    • Lower width: 480 mm (3 batteries side-by-side are 429 mm wide + 25 mm on either side for the chassis + 1 mm to make it round)
    • Height vertically: 370 mm (The tilting frame is 420 mm high. The center of the rod end holes will be 15 mm from the top of the tilting frame and 35 mm from the bottom of the frame (the rod end ball body is 30mm in diameter))
  • Wheels and Tires
    • Size: 190/55 17
    • Offset: 22 mm (measured here)
    • Camber: -2 deg

Playing around with the various parameters I can meet the goals of:

  • Ride Height: 130 mm (adjust the corners of the chassis to get this – be careful to keep your dimensions the same)
  • Track Width: 1400 mm (adjust the outermost green arrow to get this)
  • Scrub Radius: +15 mm (move the two wheel-side rod ends side-to-side to get this)
  • Kingpin Inclination: +10 degrees (move the two wheel-side rod ends side-to-side to get this)
  • Roll Center: +40 mm (this was limited by how close I could get the rod ends to the edge of the wheels without having a collision during bump and rebound)

This results in the following suspension dimensions:

  • Control Arms
    • UCA length: 435 mm
    • UCA bearing:-1.2 deg
    • LCA length: 425 mm
    • LCA bearing: +2.3 deg
    • Distance between UCA and LCA: 379 mm
  • Uprights
    • KP / spindle offset: 199 mm
    • KP / hub offset: 82 mm
    • Kingpin Length: 402 mm

The final model can be found here.

SuspensionGeometry

Here you can see the suspension’s instance center:

SuspensionRollCenterandInstantCenter

 

Wishbone / A-Arm Dimensions

Now that I have the length of the upper and lower wishbones figured out, I need to figure out how wide the wishbones will be where they connect with the chassis. Wider wishbones will be stronger and will resist torsional forces better. The biggest torsional force on the wishbones will be from braking. Narrower wishbones will be lighter and will allow for a tighter turning radius. This website has the equations for how to figure out the maximum torque on your suspension a-arm. Combining two equations we get: Brake Torque (Nm) = (Total Vehicle Mas s(kg) * Deceleration (g units) * Acceleration Due to Gravity (m/sec^2)* Static Laden Radius of the Tire (M))/Speed Ratio Between the Wheel and the Brake (r)

Using these parameters:

  • Total Vehicle Mass(kg) = 500 Kilograms
  • Deceleration (g units) = 5 Gs (Equivalent to what a Formula 1 car is capable of)
  • Acceleration Due to Gravity (m/sec^2) = 9.806 m/sec^2
  • Static Laden Radius of the Tire (M) = 0.226314 Meters (The tires are sized 190/55 17 so they are actually 17.82 inches in diameter)
  • Speed Ratio Between the Wheel and the Brake (r) = 1 (assuming the tire is not slipping, the wheel will be going the same speed as the brake)

Equation: (500*5*9.806*0.226314)/1 = 5548.08771 Nm

For reference, the Lotus 7 (“locost“) uses a 222 mm wide wishbone. My tilting frame is 200 mm across and the top wishbones will bolt to the sides of this. The Aurora MM-M12T rod ends are 16 mm wide at the ball head. So assuming the rod ends will rest against the tilting frame, the wishbone with will be 216 mm wide.

Assuming the wishbone is an isosceles triangle (which it should be to allow for the maximum turning radius in both directions), we can use the Pythagorean theorem to figure out the lengths of the legs. The equation is:

Leg = Sqrt((A^2)+((B/2)^2), where A = altitude (eg the total height of the triangle) and B = base of the triangle.

For the upper control arm, A=546mm and B=200mm so Leg = Sqrt((435^2)+((216/2)^2) = 448.206425657 mm

For the lower control arm,  A=434mm and B=200mm so Leg = Sqrt((425^2)+((216/2)^2) = 438.507696626 mm

Of course those “leg” distances are the complete distance from the center of one rod end to the center of the other rod end. The rod end’s “base to center” distance is 54 mm and the thread length is 33 mm. Assuming you thread the rod 2/3rds of the way in (to allow some room for adjustment) the total distance from the center of the ball to the edge of the wishbone leg is 65 mm. Between the edge of the tube end and the rod end is a weld-in threaded “tube end” (also known as a “weld-in bung” or “threaded insert”) and a “jam nut.” A weld-in tube end for a M12 x 1.75 RH thread (used on the v) is designed to work with 23mm OD X 3.5mm Thickness tubing. The tube end has an exposed length of 24 mm. A  M12 x 1.75 RH jam nut is 6 mm thick. So combined each leg has 65 mm for each rod end, 24 mm for each tube end, and 6 mm for each jam nut: meaning each leg should be 190 mm shorter:

  • UCA Legs: 258.2 mm long
  • LCA Legs: 248.5 mm long

Cold-drawn seamless structural round steel tubing conforms to ISO 10799-2:2011; This is a great handbook showing the various standard tubing sizes (see Table 26 for ISO sizes). Parker Steel, out of Toledo, Ohio, is the largest supplier of metric-sized metals in North America. You can also buy metric steel tubing from Metric Express and World Wide Metric.

I’m planning to use 23 mm OD X 3.5 mm Thickness tubing for the wishbones.

The problem is, in order to choose the proper tubing diameter and wall thickness it is necessary to test the design using finite element analysis (FEA) and unfortunately Solidworks doesn’t have these tubing diameters as standard weldments! So I did a little work and created a two importable libraries of standard tube weldments and uploaded them to my GrabCad page. They are located here:

 

Uprights

 

 

 

Kingpin Inclination

The kingpin inclination (KPI) is the angle between vertical axis of the upright and the vertical axis through the center line of the wheel. A larger kingpin inclination shortens the scrub radius (which can be good) but causes positive camber gain while steering (which is usually bad). As the wheel is turned, the kingpin inclination causes the chassis to rise, creating self-aligning force. Both the castor angle and the kingpin inclination provide self-centering torque, but the castor angle provides self-centering torque with good camber effects, while the KPI provides self-centering torque with bad camber effects. Thus, it is better to create self-centering torque with a higher castor angle than a higher kingpin inclination. The kingpin inclination should always be positive (with the top of the kingpin closer to the body than the bottom of the kingpin).

KPIandScrub

Some kingpin inclination numbers for high-performance cars:

  • Ferrari 355: 13.16 degrees
  • Lotus Elise: 12.0 degrees
  • Mazda Miata: 11.3 degrees
  • Ford Mustang (second generation): 11 degrees
  • Lotus 7: 9 degrees
  • McLaren F1: 9 degrees
  • Corvette C5 & C6: 8.8 degrees
  • Triumph Spitfire: 7 degrees

The kingpin inclination is dependent on the scrub radius. For my car’s geometry, with a 15 mm scrub radius, the kingpin inclination is 8.7 degrees.

 

Camber Gain in Bump

Some camber gain figures for high-performance cars:

  • Lotus Elise: 0.31 degrees per inch (25.4 mm)
  • Mazda Miata: 0.91 degrees per inch front / 0.21/0.58 degrees per inch initial/final rate

Using the Racing Aspirations model, I calculate the camber gain in bump for my car’s suspension geometry to be -0.20 degrees per inch

 

Camber Gain in Roll

Camber gain in roll is the number of degrees camber changes per degree of body roll. Ideally a car should have very little camber change with roll. Chassis Engineering explains the various ways of reducing camber gain in roll:

  1. Lower the center of gravity (CG) height
  2. Lower the roll center height by adjust (RCH) by adjusting the suspension geometry
  3. Widen the track width
  4. Increase the roll stiffness of the suspension by increasing the spring rates or adding anti-roll bars:

Using the Racing Aspirations model, I calculate the camber gain in bump for my car’s suspension geometry to be 0.90 degrees of camber change per degree of body roll.

 

Anti-Roll Bars

Anti-roll bars, sometimes called anti-sway bars, sway bars or stabilizer bars, connect the two wheels together with a simple lever arm. The longer and thinner the lever arm, the less force is transferred between the two wheels. When the car is cornering hard and the body begins to roll to the outside, the outside suspension will compress more than the inside suspension and the anti-roll bar will transfer force from the outside wheel to the inside wheel, lessening the body roll. The downside to anti-roll bars is that when you are driving straight and hit a bump with one tire, some of that bump force is transferred from the wheel that hit the bump to the wheel that did not hit the bump. This can cause the car to become unsettled and makes the ride comfort worse.

 

Spring Rate
The ideal spring rate for a car is dependent on the sprung and unsprung mass of the car as well as the desired suspension frequency.

A rule of thumb for motorcycle design (taken from Carl Vogel’s book) is that the suspension should sag 30% of the full travel under the weight of the rider (150-200 lbs).

I’m planning to use a Ducati 1198 rear suspension for my car in order to minimize the number of custom-manufactured parts. The stock rear shock absorber for the Ducati 1198 is the Öhlins TTX36. These dampers have shock and rebound dials that allow for easy adjustment. The stock Ducati 1198 rear spring has a spring rate of 90 N/mm. Because I am changing both the sprung and unsprung mass that this spring must control, it is likely that I will need a different spring with a different spring rate.

<side note rant> despite being a European shock designed for European motorcycles, the the Öhlins TTX36 shock has rod ends with 0.5 INCH diameter rod end balls. I don’t know why they use a mix of the imperial system and metric system on the same part, but it makes any engineering solution very confusing and unnecessarily complicated. What don’t we all just use the metric system!? It’s better! </end rant>

This spreadsheet allows you to calculate the proper spring rate for your car.

 

Suspension Frequency

Here are some examples of suspension frequencies from well-designed cars:

  • McLaren F1: 1.43hz front, 1.80hz rear
  • Lotus Elise: 1.50hz front, 1.63hz rear

 

 

Toe Angle

A slight toe-in at the front helps keep the steering linkages under tension, making steering more immediate.

Some toe angles of high-performance cars:

  • Lotus Elise: 0.2mm toe-out front, 1.2mm toe-in rear
  • Ferrari 355: 2mm toe-in front and rear

The toe angle is easily adjusted adjusting how far the steering rack rod ends are screwed in to the tubing ends. For this car I’m going to target a 2mm toe-in at the front.

 

Anti-Squat Geometry

 

Anti-Dive Geometry

 

Manufacturing

  • Notching / Coping the tubing
  • Tapping the threads for the rod end
  • Tig Welding

 

 

 

 

 

 

 

 

 

Other miscellaneous suspension topics:

Unsprung Downforce

Ideally, downforce should be applied directly to the unsprung mass of the car. Instead of transferring force through the body and then through the springs to the tires, wings that are mounted directly to the suspension can transfer force directly to the tires. The Lotus 49 had wings that were bolted directly to the suspension, creating unsprung downforce. The FIA banned this type of wing as a “movable aerodynamic device,” but the the idea remains sound. By changing the shape of the suspension arms to mimic upside-down airplane wings, it is possible to induce downforce directly on the tires without adding much unsprung mass. One of the easiest ways to accomplish this is to use “streamline tubing” for the suspension arms and tilt their angle slightly so they are flat on the top and curved on the bottom, thus creating downforce.

streamlinetubing

 

Inerters

Inerters, also known as J-dampers, are an important development in modern suspension design. When you compare a cars suspension to an electrical circuit, dampers act like a resistor, springs act like an inducer and inerters act like a capacitor. Resistors dissipate current flow just as dampers dissipate suspension force. Inducers resist current flow just as springs resist suspension forces. Capacitors store and release current just as inerters store and release suspension force. By adding an inerter, a car’s suspension can store up the force of a bump and release it back. This allows the use of a softer spring, which allows the car to have both a smoother ride and to leave the tire in contact with the road longer, which improves handling.

As far as I can tell, the only combination inerter/damper sold on the market today is the Penske 8786. Hopefully in the future more interters in different sizes will be sold so I can add them to the car.

 

Carbon Fiber Springs

A company called Hyperco makes carbon fiber drop-in replacement springs for suspension dampers. They are supposedly up to 70% lighter than steel springs. This might be another way to decrease unsprung mass in the future, but for now I will just use standard springs.

 

Roll Axis

On 4-wheeled cars with separate front and rear suspensions, it is possible to have two different roll center heights. If you draw an imaginary line between the two roll center heights you will see the roll axis. The roll axis is the axis about which a car rolls in a turn. If you create another imaginary line between the center of gravity at the point of the front roll center and the center of gravity at the point of the rear roll center you will create what’s been dubbed the “Mike axis” after its inventor Mike Kojima. According to Sport Compact Car, “If the space between the two lines is less in the front of the car, with an upward sloping Mike axis, the car will tend to understeer due to greater weight transfer to the outside wheels at the front of the car due to a greater amount of geometric anti roll. If the distance between the lines is greater at the front and less in the rear, the car will understeer less due to the greater amount of rear geometric anti roll giving more rear outside weight transfer. Front engine RWD cars typicaly exhibit the latter trait can can oversteer a lot despite a front weight bias. Rear heavy rear and mid engine cars also exhibit this trait, partially due to a larger rear polar moment of inertia and a smaller rear than front roll couple. A front wheel drive car is typically so nose heavy that it is pretty hard to overcome the tenancy to understeer. It takes pretty high rear roll stiffness and a bit of geometric antiroll to get these cars to rotate with reasonable wheel rates.”

Luckily, on a 3-wheeled car, there is no rear roll center, so we don’t need to worry about the roll axis and its effects on understeer and oversteer.

 

3D Cad Parts Here:

http://www.mcmaster.com/#94640a285/=vfas0m

http://www.mcmaster.com/#93839a825/=vfaxdh

http://cad.aurorabearing.com/item/all-categories/am-t-hxab-t-high-misalignment-series-male-rod-ends/hxam-7t-2

http://www.ohlinsusa.com/ohlins-ttx-25-fsae

 

 

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Will Martin is an energy analyst and expert on peak oil and alternative currencies. He is an MBA graduate of Cornell University, where he was a Roy H. Park Leadership Fellow and concentrated on studying sustainability in business through the school’s Center for Sustainable Global Enterprise. Prior to his MBA, Will worked in the energy industry, living in Singapore, Houston and Dubai. Will is a recipient of the 2012 “Pioneer Award” from the Association for the Study of Peak Oil and Gas (ASPO-USA). He currently works as a carbon trading commercial adviser in the San Francisco Bay Area. Will is a bitcoin enthusiast and in 2014 published the book “Anonymous Cryptocurrencies,” which became a #1 best seller in 3 Amazon categories and was the first book to be sold on a decentralized marketplace.

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