The ULTIMATE GTI Engineering Thread (How to Analyze Your Car)

To reply in this thread, please bring some insightful and progressive discussion to the table. PM for any questions or concerns or debates. I'll raise the disucssion and add to the thread what needs to be added. I welcome criticism as well. Once this thread is finished (Or if it ever is) I would like to ask the Mods to sticky and let the newcomers come and understand their vehicles, so its only fair to leave out unneccesary squabble. UPDATE: Stickied!


The first step to understanding your car is easy. Grab a pen and paper or computer or some sort of media to create a "list. What you ultimately want to do is start with a higher order system and gently begin breaking down each component.

Start with Components of Design:

• Propulsion
• Braking
• Suspension
• Structure
• Steering
• Design for "X"

Design for "X" is simple. Its a vague statement to lump the rest of the systems together. Such as: Safety and Convenience. I kept it simple and left it at those two...but you could do more if you wanted.

Next, Break it down into Design Concepts:

This step is a little hazy to me and I dont really understand it, but apparently it helps you actually "see" what each system wants to do and how you design for it.

• Propulsion
  
  • Potential to Kinetic Energy
  • Potential Energy Storage
  • Forward Acceleration
  • Supporting Components for Efficiency
  • Vehicle Component Energy Source
• Braking
  
  • Retard Kinetic Energy
• Suspension
  
  • Ground Continuity
• Structure
  
  • Containment
• Steering
  
  • Directional Control
• Design for "X"
  
  • Convenience
  • Safety

Finally - List each individual component that has some effective mass to the whole structure of the vehicle. (Meaning, list every damn part on your car you choose to.)

What I did in this step is list systems along with parts to sort of "group" together the weights and measurements. This way you can list systems for items you know you would never change, and you can list parts that you might change later and what you would want to see in weight savings or other performance gains. If you're completely lost about what I'm talking about, just reference the list below and you'll see how I did it. Obviously I'll miss a lot of parts, but its better to get the "Main" ones.

• Propulsion
  
  • Potential to Kinetic Energy
    
    • Block (Heads, Injectors, Rods, Cams, Valves, etc. etc.)
    • Oil Pan
    • Oil Filter
    • Intake
    • Exhaust Piping
    • Exhaust Manifold
    • Muffler
    • Turbo
    • Gas Pedal (Should Be Interior, but its a key component to energy propulsion)
  • Potential Energy Storage
    
    • Fuel Storage (Tank, Lines, and Pump)
  • Forward Acceleration
    
    • Transmission (General and to the point, you can break down further if you'd like)
  • Supporting Components for Efficiency
    
    • Radiator
    • Coolant Reservoir
    • Fan Assembly
    • Intercooler
    • Coolant Pump
    • PCV System
  • Vehicle Component Energy Source
    
    • Battery (The plastic doesnt matter....its negligible weight)
    • Alternator
• Braking
  
  • Retard Kinetic Energy
    
    • Rotors
    • Calipers
    • Parking Brake
    • Master Cylinder and lines
    • Brake Pedal
    • Brake Booster
• Suspension
  
  • Ground Continuity
    
    • Springs
    • Struts
    • Shocks
    • Upper Control Arms
    • Lower Control Arms
    • Front and Rear Sways
    • Wheels (MAKE SURE you seperate these!!)
    • Subframe
    • Various other components (End Links, Braces, etc. etc.)
• Structure
  
  • Containment
    
    • Body (I will include, Doors, windows, Fenders, Hatch, etc.)
    • **** This section, if you wanted, you can break down to individual components to see ultimate racing weight savings. Make sure you know what you want out of it before you do so.
• Steering
  
  • Directional Control
    
    • Steering Wheel
    • Tie Rods
    • Steering Assembly
    • Power Steering Pump (Lines Included)
• Design for "X"
  
  • Convenience
    
    • Interior
      
      • Seats (L and R, Front and Back)
      • Instrument Panel (Dash assembly)
      • Center Console
      • Shift Knob (Just for Giggles to see the weight savings lol)
      • Rear View Mirror
      • Interior Trim
    • Exterior
      
      • Bumpers
      • Wipers
      • Washer Fluid Reservoir (Nozzles Included)
      • Side Mirrors
      • Spoiler
      • Grille
      • Hood (Dedicated to see carbon fiber savings)
  • Safety
    
    • Head Lights (L and R)
    • Tail Lights (L and R)
    • Horn
    • Seat Belts
    • Air Bags

Any Parts that I missed? List them and I'll add....I didnt do this in front of my vehicle so I'm sure I left out some. I left out the Wheels on the first go around lol

You've successfully Decomposed your vehicle. You results may vary, but this exercise definitely helped my knowledge of what all it takes to put the vehicle together. Every component has its own "mass and contribution" to the entire design, and its amazing to see it all listed. The best thing to do now, is list it all in excel. Group what you want to, and seperate what you need to. Distinguish between left and right hand parts, front and rear. Dont forget your suspension components!!!! Once you have it all ready, sit tight and wait for the next lesson. (Trust me....its a doozy!!)

Reserved Mass Properties

Brake Horsepower (Watts) = N*Displacement(in cubic Meters)* (RPM/2)* nc*nm*nth*nv*Qhv*(F/A)*Air Density

N = Number of cylinders

Displacement = Bore*Stroke*pi/4

RPM/2 = Must be placed in Revs/Second = RPM/2 * (1/60 {s/min})

nc = Combustion efficiency = about .98-.99 on newer cars (can be calculated further, but these estimations are fine)

nm = mechanical efficiency = Function of RPM/heat/etc range of about .8-.93 (can be calculated further, but these estimations are fine)

nv = volumetric efficiency (what percentage is your TB open?)= 100% at WOT (Possibly a little more depending on the flow. Most I've seen is 108%)

nth = thermal efficiency = 0.8*(1-[compression ratio^(-.35)])

Qhv = Heating value of the fuel = 43,000,000 J/kg

Air Density = Pressure Entering / (287.2 J/kg-K * Intake Temperature)

Pressure Entering = Atmospheric Pressure * Pressure Ratio (This is a function of RPM) - J/m^3

Reserved Acceleration and Tractional forces with Optimal Shift Points

Please refer to this thread for more discussion

Now a lot of the main stuff is handed down from the big guys such as wheelbase target, Lateral and Logitudanol Force Targets, Ground height, Moment Roll, roll pitch, roll center, center of Gravity, etc. etc.

With a lot of known variables we can start solving, or at least get an idea of where we are at and deteremine suspension feasibility and performance characteristics before the vehicle is even made. Once prototyping begins, we can always tweak things to get exactly what we want.

So Lets start:

What is the one talked about topic on car enthusiasts forums? Lowering Right? Or from what I gather at least. Most people say "Stock GTI handles so good, there is no need to modify it." Right and Wrong, for everyday use right. For tracking wrong. There is literally an infinite route you can go to make your car perform well on the tracck, but at what cost to the daily driveability do you want to spend?

Theory:
I dont have any measurements for my suspension so I cant get any final numbers, but if anyone is willing, go for it.

From my suspension notes:
"A vehicle with a suspension is not a rigid body. The unsprung mass stays (mainly) on the ground. The sprung mass does not roll about the center of gravity. The sprung mass rolls about a kinematic point known as the ‘roll center’ which is defined by suspension geometry. (For preliminary design, without other domain knowledge, take roll center to be at height of axles.) If the roll center is above ground, then the lateral force on the tires in a turn must be directed towards the turn’s center of rotation in order to maintain the vehicle’s equilibrium. The tires scrub to the outside to generate this force. If the roll center is at the ground, there is no tire scrub. If the roll center is below ground, the lateral force is oppositely directed, and the tires scrub into the turn. This causes a break in traction, and the vehicle motion becomes unstable. Roll centers are placed enough above ground that no combination of driving or failure will cause them to move below ground. Roll centers in rear suspension are usually placed higher than those in front suspension so that the rear will be more stable than the front, and the rear will not want to over-rotate (oversteer)."

How do you calculate the roll center?
Moment of Roll (How hard you're vehicle rolls) = Roll Stiffness * Roll angle

Roll Stiffness = Front Roll Stiffness + Rear Roll Stiffness = FRS + RRS

FRS = 0.5 * Wheel Rate * Front Trackwidth^2 + Stiffness of Front Sway

RRS = 0.5 * Wheel Rate * Rear Trackwidth^2 + Stiffness of Rear Sway

*Sway thickness can be forund on the internet if you google Sway stiffness formula

*Assume your wheel rates are the same on each side

Moment of Roll = Sprung Mass * Gravity * (D) * Roll Angle + Sprung Mass * Laterall Acceleration * (D)

Lateral Acceleration = Speed into the turn / Radius of the Turn

(D) = Height of center of gravity above roll center (if roll center is above CG, d < 0 )

*This part is a little hard to determine WHERE exaclty the roll center is, but I will help you. From Happian-Smith (An Introduction to Modern Vehicle Design, 2002):

Front:
"The Roll center for a MacPherson Strut suspension lies on the upper defining line of the moment of inertia of the upper mount of the strut perpendicular to the strut axis." I'll discuss further:

The front roll center of a car with the Mustang's MacPherson strut suspension can be found as follows:

- Draw a line at an angle of 90 degrees from the top of the front strut
- Draw a second line through the lower control arm. The point where these lines intersect is the instantaneous center
- Draw a third line from the instantaneous center to the center of the tire contact patch. The point where this third line crosses the car's centerline at the roll center.


http://www.miracerros.com/mustang/t_rollcenter.jpg

This will be your (D) for the front.

Rear:
"The roll center for a trailing arm suspension lies in the ground plane on the center line of the vehicle" MEANING...its basically on the ground. Your (D) would equal the distance from the COG to the ground.

Just connect to the two dots...and you get your roll axis:


http://www.miracerros.com/mustang/t_rollaxis.jpg

This is what your car rolls about when you turn. FYI that is just an example....but you get the idea.

What does this all mean?

You know your roll stiffness, now you need to find your Roll Moment, but in order to do that you must solve for your roll angle. AND in order to do that, you must solve an average roll center between the front and rear. Shouldnt be hard, Front + Rear divided by 2. Then just rearrange that roll angle formula:

Roll Angle = [Sprung mass * Laterall Acceleration * (Daverage) ] Divided by [Roll stiffness (Front+Rear) * Sprung Mass * gravity * (Daverage)]

And guess what? We're not done. You can now take this formula and find your wheel deflection:

Wheel Deflection = roll angle * trackwidth / 2, You can homogenize to either the front or rear, but then you'd have to break up the roll angle formula and just use the (D) for each specific case.

Wheel deflection of the front = roll angle of the front * front trackwidth / 2
and ditto for the rear.

What does this Ultimately entail?
Well...you can seen it can get pretty hairy, but as long as you pace through it, its not so bad.

I can safely say now, you can see theres an affect going on when lowering your vehicle. When lowering you drop the effective roll angle closer to the center of gravity and you stiffen the roll. Meaning, you can have hard springs and hard dampers and never see your car roll. Obviously the more roll, the more wheel deflection you get thus removing how much power you put to the ground when coming out of a turn. Thats it.....thats the whole idea of wanting a stiff suspension while tracking.

Now for daily driving, you can sacrifice some stiffness for some body roll. This helps for a smooth ride and happy passengers. I myself use Bilsteins on my new MKV but they're a little stiff. But DAMN do they handle nicely. They deflect the wheel barely an inch coming hard into turns. Do I track the car much? Not really, so in my honest opinion, I will be getting rid of them and sacrificing that performance for a better ride. But others will do differently.

Obviously all the equations are limited to suspension geometry. Meaning, you cant slap the wrong hardware and expect ultimate performance. Its all a matter of balance.

Lateral Load Transfer

This is a bit harder to explain. You have many many many many factors to consider. But its a good idea to touch on this for those you have a grasp on the concept.

Here are some references to read if you're curious:
http://en.wikipedia.org/wiki/Weight_transfer
http://www.neohio-scca.org/comp_clinic/hand_out_reprints/LoadTransfer%20reduced%202.pdf

Heres just a reference formula to blow your mind:

Front Turning Force = [mass of the vehicle * distance between CG and front trackwidth* Lateral Acceleration * height of CG above ground] / [wheelbase * front trackwidth]

Front Turning Force = All of that mess above + [Roll stiffness * Sprung mass * Lateral Acceleration * (Dfront)] / [front trackwidth * (roll stiffness - sprung mass * gravity * (Dfront))]

Ugh......then you can do the same for the rear. Now that you have both Front and Rear Turning Forces you can do the following:

If, Front Turning Force + Rear Turning Force > (vehicle mass * gravity) /2

Then the vehicle rolls over.

Eventually you'll get to a point where your suspension can handle the force its taking from the turn, but your tires cant. Keep that in mind when you're tracking the vehicle. Always have some nice sticky tires.

I KNOW I've missed some stuff and probably confused the hell out of most of you, but people have wanted to see if for quite some time. Any questions? Post them!

This should offer some insight as well:
http://forums.vwvortex.com/showthread.php?1448594-The-Suspension-Forum-FAQ-Thread

Enough chit chat....Lets continue. Again, I will keep this vague with as little mathematical derivation as possible. But, should you want to dive further I would definitely brush up on differential equations and basic physics.

I have found my interest lies within the damping aspect to determine my ride quality.

Relationship between spring and wheel rates

In general the relationship between spring deflections and wheel displacements in suspensions is non linear, which means that a desired wheel-rate (related to natural frequency) has to be interpreted into a spring-rate.

Suspension or motion ratio = Spring force/ Wheel force ******(Not the same as spring rates or wheel rates)

To find ANY motion ratio, jack the car up and let the suspension hang. Measure the spring length at this very moment. Then use the jack and deflect the wheel a given amount of inches. Once you do so record that and then measure spring length again. Use those numbers and relate it to this newly derived formula:

Motion ratio (R) = [Final spring length - Intial spring length] / Wheel deflection

Normally, you will know your spring rates. its as easy as searching on google. If you know your spring rates, then you can relate them to a spring energy formula....for the sake of no confusion I've derived it into its simplest form:

Wheel rate = Spring rate / [Motion ratio^2]

Motion ratio results from the same kinematic suspension analysis that gives camber gain and roll center. Note that R is usually greater than 1, so the wheel rate is less than the spring rate. R is not constant; it varies as a function of v. But on an front handling car, it will be close to the ride height value at both full bump and full droop. Once the desired kw is known, and R has been determined from a candidate suspension geometry, ks may be determined. Note that the spring’s own free length (i.e., under no load) corresponds to full droop and not to ride height.

Dampening and Natural Frequency

From Happian Smith:
Frequently called shock absorbers, dampers are the main energy dissipators in a vehicle suspension. They are required to dampen vibration after a wheel strikes a pothole and to provide a good compormise between low spring mass acceleration and adequate control of the unsprung mass to provide good road handling.

Might Wanna Look at Wiki too.....Click Me

Twin tube vs. Monotube


Good Read: Twin Tube vs. Monotube....CLICK ME

Basically Twin tube = comfort; Monotube = Performance

Back to the good stuff. While skipping the boring and tedious derivations, the undamped natural frequency is:

Nat. Frequency (omega) = Square root(wheel rate / sprung mass)

If the wheel rate is maintain constant, the natural freq decreases as the payload increases. It is possible to determine a variable wheel-rate which will ensure that the natural frequency ramains constant as the sprung mass increases. (More on that later)

Effective corner damping coefficients may be set by the damping ratio:

damping ratio (ζ) = effective wheel damping ratio / (2*omega*mass of the vehicle)

- Critical damping (ζ=1) is the boundary limiting oscillation after disturbance.
- Slightly overdamped (ζ=1.2) will keep the wheels hard-pressed to the ground.
- Slightly underdamped (ζ=0.6) will allow more rapid response to disturbance say rolling into a turn) without much oscillation.
- More underdamped (ζ=0.35) will allow rapid wheel deflection, such as necessary to follow a rough surface.

This part is hard because companies do not give these values. But you can calculate a critical damping ratio and go from there. You can see that there is A LOT of fine tuning that goes into this.

Look at this pic:

Normally you want to find that range of overshoot to not allow the car to go haywire when you hit a bump, but also you dont want to car to overshoot and bounce like a pogo stick when hitting a bump and returning on the rebound. Again, you can solve for which damping ratio you'd like and find a coefficient of damping and go from there. You might be able to ask companies for their values, but be warned, they might not give it to you.

Happian-Smith:
In dealing with road surface undulations in the bump direction (damper being compressed) relatively low levels of damping are required when compared with the rebound motion(damper being extended). This is because the damping force produced in bump tends to aid the acceleration of the spring mass, while in rebound an increased level of damping is required to dissipate the energy stored in the suspension spring.

What is the ultimate design? A controllable suspension (DCC) that electronically controls the adjustment forms of the basis of improving ride and handling. AKA Sport Standard and Comfort. Most companies design for the middle, but what the user wants to decide between tracking and daily driving? This system provails.

The biggest is when you chose a static spring and shock setup that has to balance the two: Comfort and Sport. Thats where multivariable input shocks such as Koni FSDs come into play. Basically just a valve that has high limits that soak up the major bumps in the road, but at slow compressions, such as during turns, they act as a performance shock. Still....when does the valve open? Thats left for some interpretation and subjective reasoning to deteremine "ride quality"

Reference PDF


An objective approach to ride quality will be discussed further, when I can collaborate my notes a little better....Stay tuned.......

Click for Original discussion thread

I'll premise this by saying, you do what you want at your own risk. I'm no way responsible for any wrong doings you do when modifying your car. Dont come to me complaining your rims warped and its my fault. I'm just creating a learning enviorment to better help understand our cars and help facilitate technical discussion over a forum that loses sight of its principles, sometimes.

Some vocbulary that will be mentioned:
Mass Moment of Inertia
Wheel Diameter (Not Rim Diameter)
Angular Velocity and Accleration
Frictional Forces
Lateral Forces
Tire Patch Width
Skid Ratio
Slip Ratio
Peak and Slide Coefficients
Slip Angle
Vertical Loads
Cornering Stiffness
Camber Angle

This thread will cover to theory and physics behind to a great debate:

Should I go lighter weight on my wheels?

The question I would then ask to you would be, well.....how much do you truly appreciate your suspension? Do you track a lot and really stretch the limits of your vehicle? Or do you just want better looking rims? If you want better looking rims, throw all caution to the wind and by the ones that you think look the best while the rest of us out perform you on the track. Nice 19s btw, how much do they weight?

Why does lighter wheels mean better performance?

A Few Facts to consider

1. Weight
   • Wheelset and part of suspension are “unsprung weight”, which by definition cannot respond to the spring and damping of the suspension system (this is bad).
2. Performance
   • Maintain Ground Contact
     • A tire that is not touching the ground is not accelerating the car or controlling the car.
     • Without ground contact a car is a projectile, losing speed and out of control
   • Limiting Lateral Load Transfer
     • A car in a turn puts more vertical load on its outside tires and less on its inside tires
     • The lateral resistance of a tire depends on the vertical load on that tire, but not linearly - the more and more vertical load on a tire, the less and less lateral load is generated as a result
     • Therefore, its best to keep the vetical load as evenly distributed as possible to maximize turning ability

Traction and braking forces
Longitudinal slipping and sliding
All tractions and braking forces are associated with slipping of the tire patch over the ground. The tire rubber deforms under friction load on the ground, this deformation integrates from the leading edge of the tire patch to the trailing edge, and resolves into slip (higher velocity than the vehicle for acceleration and steady driving, lower velocity than the vehicle for braking) as the tire patch lifts off.
If the local slip exceeds the locally-available coefficient of friction (velocity dependent), then the tire patch breaks loose and slides. Tire slide is a relative velocity between tire and ground at the leading edge of the tire patch.

Slip ratio (acceleration, driving)

i = 1 - [V/(Rw*ω)]

Angular Momentum

L = Iω

where i is slip ratio, V is vehicle speed, Rw is wheel radius (free – not compressed), and ω is wheel angular velocity.

Angular Momentum (L) is a function of wheel angular velocity and Mass Moment of Inertia, which ultimately is a function of the mass of your wheel.

For this case, we'll assume a wheel is a SOLID cylinder. Its a fortified assumption and will work well in our calculations. Theres actually two different mass moments of interia for this case, but we'll only take into consideration the axis about the wheel rotation.

Mass Moment of Intertia = [Mass of the wheel * (Radius of the entire WHEEL)^2] / 2

Simple? This is where the 17 vs 18 topic comes into play. Effectively, the entire wheel diameter remains the same between the two wheels, however, the bullk of your weight is 1" further into the axle with 17" rims, as opposed to 18s. Granted, if the mass of your 18s are lighter than stock, you might be able to perform better.

If you wanted, you could almost weigh both sets of tires, and detract that from your overall formula and find the effective 17 vs 18 calculations. You'll immediately see a difference.

Now, a heavier wheel would create a greater moment of interia and inevidtably create more angular acceleration, thus creating more downward force on the tire patch, THUS creating more traction THUS creating better acceleration times. A smaller diameter wheel would cause more wheel spin, because you've effectively reduced unsprung weight allowing for more torque to be transfered to the tire patch.

But thats only in a straight line. What about during a track event?

Well, thats where the lighter weight wheel shines. Every rotation aspect of the wheel whether it be turning, sliding, spinning, +/- camber is a function of rotation mass moment of intertia. The heavier the wheel the more reluctant it wants to rotate, spin, etc. etc. This causes more load and more forces traveling through the suspension and cause you to lose handling performance. Its always better to run lighter wheels if you have the opportunity.

Overall, where are your gains seen most? You can consider sticking to the stock heavy wheels for some traction, however, the pros outweigh the cons.

Reference PDF

Reserved Steering and Braking

Reserved Power plant Auxillary

Flywheel and Clutch assembly - both energy storage and kinetic components

UGH, I need to get around doing this......

Would anyone object me for putting up the fomulae to interpret yourselves and whenever I get the chance for numbers to insert I can edit and repost?

I think it might be fun for another user to try it out. I can supply as much help as needed and even MATLAB code if neccessary.

A tiny dicussion about stock IHI/K03 Turbos

Stickied elsewhere, but its good to have it here, as well.

grambles423 said:

UGH, I need to get around doing this......

Would anyone object me for putting up the fomulae to interpret yourselves and whenever I get the chance for numbers to insert I can edit and repost?

I think it might be fun for another user to try it out. I can supply as much help as needed and even MATLAB code if neccessary.

Click to expand...

:thumbup:
details of what you are refering too?

GTIwannagofast said:

:thumbup:
details of what you are refering too?

Click to expand...

Everything. I'm just gonna paste what I've already written and put as much theory and general stuff in as I can.

I was going to provide numbers and a realistic approach to all of this, but with having a job 7:00-5:00 its hard to have the motivation to do anything when I get home. When you're doing this at work you kind of want a break from it sometimes because my brain is 100% while I'm here. lol

grambles423 said:

Everything. I'm just gonna paste what I've already written and put as much theory and general stuff in as I can.

I was going to provide numbers and a realistic approach to all of this, but with having a job 7:00-5:00 its hard to have the motivation to do anything when I get home. When you're doing this at work you kind of want a break from it sometimes because my brain is 100% while I'm here. lol

Click to expand...

:thumbup:
i have no objection to a math/engineering information dump. i have a baby at home, so motivation at my house is at an all time low as well, so i doubt i'll be dedicating much time number crunching. but, i am curious to see where your thoughts are (regarding this thread).

Bump