Suspension Design Spreadsheet Manual
By Dennis Schøler Pedersen
Disclaimer
While these equations are nothing new, have been used by automobile manufacturers and racing teams for decades and have been thoroughly tested, there are many factors which can affect your car's suspension and the accuracy of the spreadsheet results including bushing deflection, shock absorbers, the accuracy of your computer's math co-processor, tolerance "stack-up" and steel and workmanship quality. Leaf springs, especially, are not easily quantifiable due to the different ways they can be constructed. For these reasons, I cannot guarantee the accuracy of the final results of these spreadsheets or how the parts you may purchase or build according to these results affect your car and its handling.
Also, while these spreadsheets do a great job of meeting the parameters you set them, there may be times when you are better off favoring other aspects of your car. For instance, front-engine, rear-wheel drive cars often benefit from a stiffer front sway bar -- even though you might think it would cause the car to understeer excessively. The reduction in body roll often helps the grip of the front tires more than the increased weight transfer hurts because the tires are flatter to the ground. Plus, the stiffer front sway bar can help "get the power to the ground" better exiting turns.
It is divided into sections that correspond to the sections in the spreadsheets. It is strongly recommended that you read the ENTIRE manual before you start working with either the spreadsheets or your car. It uses figures of suspensions as guides to show you where to make the measurements the spreadsheets call for.
The first section "Existing Suspension Design" explains how to measure the characteristics of your current suspension. It also explains some of the basic theories behind suspension tuning.
The second section "New Suspension Design" helps you determine how you want your new suspension to behave.
"New Suspension Component Design" is similar to the first section. It is there to give you a workspace to design new suspension components using the numbers derived in the "New Suspension Design" section.
Then, you can measure your car (forms are available which make it easier to make the correct measurements, and organize them for easy entering into the spreadsheet), open a spreadsheet and start entering your numbers. The spreadsheet will calculate the characteristics of your suspension automatically, using equations built into it and the numbers you've entered. At the end of this manual there is a section "Special Applications" which assists you in using these spreadsheets to go beyond their usual limits.
You can use these spreadsheets without any difficulty, provided you already know the basic operating features of Microsoft Excel. No advanced knowledge is required beyond that. If you are not familiar with Excel's operating features, consult the documentation for it. Then familiarize yourself with this manual and follow the directions!
All dimensions entered MUST be in either decimal inches or pounds, except when otherwise indicated.
After downloading the appropriate spreadsheet file for the suspension type you'll be working with, make a duplicate of the downloaded file, give it a suitable name and you're ready.
Cell protection is used to prevent accidental corruption of the spreadsheet's cells. In some cases, as will be explained later, you may wish to lift that protection. In these cases registered users ONLY can simply access the protection feature of Excel and use the password issued to them to unlock the spreadsheet (see Purchasing Spreadsheets And Manuals). Make sure to lock the cell protection when you are done to prevent accidental deletion of other cells. Note that when you enter numbers in the cells which ordinarily are used by the spreadsheet to automatically display results, you are deleting the equation within it. That is why it is important to always keep backup files.
The spreadsheets are arranged in two columns so that all information pertaining to the rear suspension is in the left-hand column, that for the front suspension is in the right-hand column. Figure 1 shows a sample spreadsheet with some of the numbers already entered. Note that the right-hand column has no numbers entered yet, so the result isn't displayed.
It is important to understand that you often MUST enter ALL the numbers pertaining to a given calculation before a result can be displayed by the spreadsheet. There are times when you will have to enter numbers for parts your car doesn't even have -- as is the case for sway bars. The reason for this is usually that the spreadsheet has to divide a number by "0" which causes an error message. Instead you may have to enter arbitrary numbers in the place of actual ones -- this causes no problems and is merely a limitation of the host programs. This will be explained in greater detail later.
The first step in developing your car should be to reach a thorough understanding and appreciation of how it works now. You might be surprised at how well the engineers designed the stock suspension. Though you may disagree with some of their design philosophies, keep in mind that they are working under considerable constraints -- such as trying to keep millions of customers happy -- whereas you can redesign the suspension to suit no one's needs but your own.
Read this ENTIRE section before you start working with the car. This section involves making careful measurements of it. Some, like coil spring "free length," may require disassembling parts of the suspension to accurately make them. You should make those not requiring disassembly first, such as the car ride height etc. That way you won't have to disassemble the suspension more than once and the car will be ready for you to install the new parts.
To make it easier to keep track of all the required measurements you need to make of your car, forms are available for downloading which you can fill out as you work with the car's suspension. You must first download the Adobe Acrobat® Reader application to view and print the Acrobat "PDF"-file formatted forms. They are named similarly to the corresponding spreadsheets so it is easy to determine which form you should download. Note that ALL dimensions must be in either decimal inches or pounds unless otherwise noted.
When entering numbers in the spreadsheet it is best to do them in the order they are listed, but not required -- it will fill in the blanks as soon as it has received ALL the necessary numbers from you.
Spring Rates
These are measured in pounds/inch (lbs/in). For instance, a spring rated at 200 lbs/in requires 200 pounds on top of it to compress it by one inch. It is best to measure the springs by testing them in a spring rate tester, especially if you are dealing with leaf springs, since small errors can be compounded easily. You can then enter the numbers in the cells usually used by the spreadsheet for displaying the results. To do so you must unlock the spreadsheet first -- see "Using The Spreadsheets." You are still REQUIRED to enter the number of coils and active coils, as well as the free length, if they are coil springs. A different way to measure coil spring free length than that shown in Figure 2 is to measure only the length of the "active coils" as shown in Figure 5. That way, you can eliminate the variable resulting from odd-shaped coil ends where the springs seat.
If you don't have access to a tester, you must make ALL the measurements shown in Figure 2 for coil springs, Figure 3 for leaf springs and Figure 4 for torsion bars. Then enter the resulting numbers in the corresponding cells of the spreadsheet. The wire diameter and leaf thickness dimensions are very critical -- use a micrometer or good calipers to make this measurement. The spreadsheet will automatically calculate the spring rates for you as you enter the numbers. See also "Special Note About Leaf Springs."
Installed Coil Spring Rates
Not all the coils of coil springs are "active," that is to say, the ones on the ends are only there to act as the connection between the spring and the spring seat -- they don't move or flex -- so the installed spring is stiffer because it has fewer coils. Determine at what point the spring is free of the seat and start your count from there. See the example in Figure 5.
Sway Bar Rates
These are easy to measure -- see Figure 6. As for springs, the most critical dimension is the wire diameter. Some cars use tubular sway bars -- if your car uses one, enter the inside diameter (I.D.) in the space provided, otherwise leave it blank. If your car has less than 2 sway bars, you MUST still enter values in the cells in that part of the spreadsheet meant for the center width and length, inner pivot to sway bar pick up number and the leverage numbers for the spring leverage (any number will do), just omit a value for the wire O.D. and tube I.D. where there is no sway bar. When you've entered the dimensions the spreadsheet determines the actual rate of the sway bar(s) for you. If your sway bar is curved, measure the "center width" and "arm length" ALONG the curves so that the total length of bar is measured -- using a tailor's tape measure is helpful since it can follow the contours. The "length" is measured in a straight line.
Leverages
Leverage is a simple principle that describes how force can be made greater or less depending on where it is applied on a lever. Figure 7 shows a very simple lever and the ratio of leverage. If the hand moves 2 inches the weight moves only 1 inch. Also, the weight feels like only 5 pounds instead of 10 to the person doing the lifting. With a spring, the force required to compress it is the installed rate of the spring divided by the square of the leverage (since the force is halved, PLUS, the amount the spring is compressed is ALSO halved).
Suspensions usually have leverage on the springs, shocks and sway bars and this affects the effective stiffness of them. It is best to measure leverage on the car since this eliminates some sources of errors. You then enter the resulting numbers in the cell normally used to display the results (after unlocking the spreadsheet first -- see "Using The Spreadsheets"). The following method is easy and works great (make sure the car is on a flat, level surface):
Measure the normal ride height of the car at the end you are working with as close to the wheel center line as possible as shown in Figure 11. Then measure the length of the installed spring AT RIDE HEIGHT and, if measuring sway bar leverage, the distance of its end link from a suitable point on the BODY of the car as directly above it as possible. Now, add weight to that end of the car centered directly over the axle. Measure the new ride height, the new installed length of the spring and the new distance of the sway bar end link from the body. Subtract the second numbers from the corresponding first numbers to find the amount each distance changed. Then, find the ratio of leverage by dividing the change in ride height by the change in the other two dimensions respectively. The resulting numbers are the leverages of the wheel over each part as a ratio to "1."
If you can't measure it that way, you must instead let the spreadsheet calculate the leverage by making several measurements and entering the numbers in it. Figure 8 shows where to measure some common suspension types. For some suspension types, like leaf springs and some torsion bars, the leverage is always 1:1. In those cases, you MUST still enter the numbers other than inner pivot to spring pick up so that the leverage on the sway bars can be calculated.
Some suspensions have the sway bar mounted on a different arm than the spring (for instance a beam axle with coil springs where the coils rest on the trailing arms but the sway bar attaches to the axle). In those cases you MUST do the following; First enter the numbers to calculate the spring's leverage. Then, after the spreadsheet has displayed a value for the spring leverage, unlock the spreadsheet (see "Using The Spreadsheets") and merely re-enter that number in the results cell that was displaying it before. Now, go back and enter values in the spring leverage cells that are appropriate to calculate the sway bar leverage. Enter the "inner pivot to sway bar pick-up" in the sway bar leverage cell and its results cell should display the correct leverage for the sway bar.
In a manner similar to that used above, if your car has 2 sway bars at the same end of the car, you'll have to first measure one, calculate its WHEEL rate, then measure the other's wheel rate and add the 2 rates together. Enter this total value in the results cell for the sway bar wheel rate.
Wheel Rates
These are the stiffnesses of the various suspension components measured at the wheels -- which is a function of the rates and the leverages. The wheel acts just like the hand in Figure 7. The spreadsheet calculates them for you if you enter all the required measurements. It is best, though, to measure the actual wheel rates on the car -- even if just to double-check the results of the spreadsheet -- using this method;
Measure the ride height at one end of the car (Figure 11). Then, add a known weight to that end of the car, centered directly above the axle, sufficient to lower its ride height by at least one inch (make sure you don't bottom out the suspension!). Now measure the new ride height and subtract it from the first. Then, divide the known weight by that number. This gives you the total spring wheel rate at that end of the car. Dividing this rate by two gives you the spring wheel rate per wheel. Note that sway bar rates are NOT measured in this test since they don't resist vertical motion of both wheels together -- they resist only motion of the wheels in opposite directions (as in a turn). Then measure the wheel rates at the other end of the car by repeating this test on the other end of the car in the same manner.
Take care to make the measurements as accurately as possible. If this test indicates a large discrepancy between the wheel rates calculated in the spreadsheet and those actually measured, go back and double check ALL the numbers you've entered so far, then repeat this test. Usually, if there is a problem, it is a mistake in measuring leverage or wire diameters or the part may be made using a special alloy or heat treating.
Leaf springs with more than one leaf usually have a progressive rate. This means that their rate increases the more they are compressed. The reason for this is that leaf springs are often assembled so there is a gap between each leaf at normal ride height -- only the top leaf is active most of the time. When the top leaf is compressed more, it comes in contact with the next leaf below it -- which then adds more resistance. Furthermore, the friction between adjoining leaves can throw off the results even more. The rate calculated by the spreadsheet is the maximum rate of the leaf spring assembly. You may be better off measuring the spring rate using the method discussed earlier (at normal ride height), then entering the rate in the spreadsheet. After you've calculated new springs (as shown later), find the ratio of the new rates vs. the old measured rates and order new springs based on that ratio. For example; if your old measured wheel rate was 230 lbs/in, and the spreadsheet recommends a new rate of 320 lbs/in, order new individual leaves that are each 139% as stiff as the old individual leaves were.
The spreadsheet calculates and adds up the wheel rates of both the springs and the sway bars to derive this number. It represents the ability of your car's suspension to resist body lean (roll) in turns. Since body roll is of great interest to car handling it can be seen that this number is very important. You can use it later to decide if you need to increase your car's total wheel rates and by how much in the "New Suspension Design" section.
Total Wheel Rate Ratio Front/Rear
This ratio is perhaps the second greatest factor in the handling balance of the car (understeer vs. oversteer) -- the most important factor is the weight each tire supports. Higher wheel rates in the front generally promote understeer (front tires slide first in a turn). Higher rates in the rear generally promote oversteer (rear tires slide first so you spin out).
Car Weights
Weight is important because suspension "stiffness" is a function of the weight each spring supports. More weight effectively softens a suspension. "Unsprung weight" is weight that follows the road exactly -- like wheels, tires, hubs and brakes. "Sprung weight" is weight above the springs -- like the car body, engine etc. Some parts, like suspension parts, can be partly sprung weight, partly unsprung. How much of each is sprung or unsprung can be related to leverage. See Figure 9 for examples of how unsprung weight is calculated.
If you have access to wheel scales, which are placed under each wheel to measure the total weight on each wheel, you can weigh the car exactly as it is driven with the optimum level of fuel in the tank, spare tire removed or whatever. You can even weigh the car with the driver seated and design springs that take into account the resulting weight distribution (see "Special Applications"). Enter the weights measured in the appropriate cells minus the unsprung weights PER WHEEL after unlocking the spreadsheet (see "Using The Spreadsheets").
If you don't, you can use the numbers from magazine tests, manuals etc. to get pretty close. Enter the total weight of the car first, then the percent of weight distribution at each end, then the unsprung and removed weight PER END. "Removed weight" is simply a place for you to enter the amount of any weight you may have removed that would make it weigh less than the stock "curb weight" you entered earlier. If you add weight, make the number negative -- to do so it may be best if you precede the number with a wordspace (one stroke of the space bar), then the minus sign (-).
For circle track and other cars that use "weight jacking" (unequal weight distribution from one side of the car to the other), see the "Special Applications" section.
This is the only measure which can numerically indicate the comfort level of a car's suspension. It is a function of the wheel rates of the springs and the weight on each wheel. It is measured in "cycles per second" which means that a suspension with a frequency of 1 will move up and down once per second after hitting a bump -- one with a frequency of 2 will move up and down twice per second. This is a constant amount no matter how big the bump -- a bigger bump simply causes it to move further and faster, not more times per second. Luxury cars tend to have natural frequencies in the 1 cycle/second range, while high-performance street cars generally don't exceed 2 cycles/second. The spreadsheet calculates the natural frequencies for you, based on the wheel rates and weights you've previously entered.
Ride Height
Since only coil springs are not easily adjusted for ride height, only they are given this calculation. Other suspension types can use simple adjustments to achieve the desired ride height.
Measure the ride height of the car as shown in Figure 10. You must also enter the outside diameter of the tires you are using. These numbers are important if you will design new coil springs in the "New Suspension Design" section because they are used to calculate their free length.
Favored Speed Of Car
The difference in natural frequency between the front and rear suspensions, and the wheelbase length, determine the "favored speed" of the car. The front and rear suspensions will generally complete the first full up and down motion at the same time after hitting the same given bump when driving at the speed displayed by the spreadsheet. This speed is that for which the suspension is most effective at dealing with bumps. Poorly matched springs often result in "pitching" of the car at some speeds, usually caused by the natural frequency of the front suspension being too high compared to the rear. This problem is often typified by a very high, or even negative speed in this cell of the spreadsheet. Note that things like shocks and tire pressures can affect pitching too. For instance, excessively soft rear shocks or low rear tire pressures can cause the rear of the car to bob up and down, even though your springs may be matched properly.
You should now be well acquainted with your car's existing suspension characteristics and prepared to make some informed decisions about what, if anything, to change. The numbers you enter for "desired" characteristics are called design "parameters" in here.
Desired Favored Speed Of Car
Deciding on this parameter is easy -- just decide at what speed you will most need to have a good ride. If there is a particularly bumpy section on the track you usually race at, you might want to find out how fast you are travelling over it and favor that speed. Or just favor the average speed you drive at.
Desired Total Wheel Rate Ratio Front/Rear
If you like the handling balance of your current suspension, don't change this from the number displayed earlier. If you think it under- or oversteers too much, you should decide on a new ratio. If it understeers too much, make the "front" number smaller; if it oversteers too much, make the number higher. The best thing to do is to experiment with your current suspension. Try removing the sway bar at the end you want to have stick better, then drive it that way. If you like it, calculate the resulting ratio using the spreadsheet and enter that value here. If not, make a bigger change and test that setup.
If you really don't know where to start the following table can be used. It is meant ONLY as a GUIDE and gives typical ratios that I have found work well on competition cars I have personally tested and driven. These are here ONLY as examples and you should NOT assume that they will work in the same way for your car. This is, unfortunately, the least scientific part of suspension tuning. Too many things can affect how a car handles to make it easily reduced to a number, but at least you'll have a good starting point. Front engine/rear wheel drive cars often shift from extreme oversteer under power to severe understeer in turns. For that reason I don't feel it would be appropriate to list any value -- you'll have to decide on a ratio that best suits your driving style, track conditions etc.
| Car Type: | % Weight Front, Rear: | Total Wheel Rate Ratio Front/Rear: |
|---|
Front wheel drive
Mid-engine
Rear engine | 61%, 39%
44%, 56%
39%, 61% | .4 : 1 to .8 : 1
1.2 : 1 to 1.4 : 1
1.4 : 1 to 1.6 : 1 |
Desired Total Wheel Rate
As mentioned earlier, this parameter is very important to racers since it affects how much the car will lean in turns. Body lean (or roll) is not very bad by itself, but it can cause problems if too severe. Body roll usually causes the wheels on cars with independent suspensions to run at an angle to the ground. This reduces the effective grip of the tires in turns. If your car has an adjustable suspension increasing the negative camber of the wheels helps keep the wheels that are facing toward the outside of a turn flatter to the ground. But, negative camber can cause the wheels to the inside of a turn to lose traction since they will be running at a greater angle to the ground than before. The stiffer your car's suspension is (the higher the total wheel rates) the less your car will lean. Don't try to make the suspension so stiff that it doesn't roll at all, though. The stiffer the suspension is, the less traction you'll have on bumps -- and they don't have to be big bumps to cause problems either. You should instead try to determine the MINIMUM total wheel rates your car can have that won't result in excessive body roll.
Take some photos of your car at maximum cornering speeds to find out how much it leans now. A good rule of thumb is to limit body roll to between 1 and 4 degrees, depending on the suspension type. If you have lots of room for negative camber -- or have a suspension with favorable geometry -- you can get away with more body roll. If you use a "tire pyrometer" for testing (as described in many books about suspension tuning) you can use it to determine whether you have enough room for negative camber or not, and whether the car leans too much. Body roll becomes less tolerable with wider wheels, because you can't get the maximum benefit out of them if they are running at an angle to the ground. If your car leans twice as much as you want it to, double your existing total wheel rate. But there is a good chance that your car will be able to corner faster with its new suspension -- which increases the body roll -- so it might be a good idea to make the total wheel rates higher than you think they need to be, especially if your existing suspension allows a lot of body roll.
Desired Rear Natural Frequency
Here you must make a decision about how much discomfort you are willing to put up with. An excessively high natural frequency can result in a car that is almost unbearable to drive. As mentioned before you should reconsider carefully any suspension you design that requires a natural frequency below 1 or above 2 cycles/second. All-out competition cars can often use higher frequencies than others since they are usually run on smooth surfaces. I've even seen some successful autocross cars that had frequencies well above 3 cycles per second! They were trailered, of course.
The advantage of selecting a high natural frequency is that it allows you to rely less on sway bars and more on springs to achieve high total wheel rates. Sway bars have the disadvantage of causing the inside wheels to lift -- which can cause wheel spin exiting turns under power if the bar is on the driving wheels, as well as worse braking into turns etc. On the other hand, sway bars have a greater effect on handling balance (understeer and oversteer) than springs do. This is because sway bars reduce the grip of the tires at one end of the car to balance the handling. They not only can reduce the grip of a tire facing the outside of a turn by loading it more, but can also reduce the grip of a tire facing the inside of a turn by lifting it to the point where friction -- and grip -- is reduced. Also, sway bars have little effect on the natural frequency, so if you want a smoother ride with less body roll you can enter a low natural frequency and the spreadsheet will achieve the total wheel rate you entered earlier by recommending stiffer sway bars than it would if you entered a high natural frequency.
The rear natural frequency you enter will be used by the spreadsheet to calculate a natural frequency for the front suspension based on the car's wheelbase and the desired favored speed you entered.
Desired Ride Height
If you are working with coil springs you also have to enter the desired ride height and the outside diameter of your new tires. There can be good reasons to change this parameter. A lower ride height gives your car a lower center of gravity which means less body roll and weight transfer in turns. Don't go overboard -- sometimes the lower ride height can cause not only a greater likelihood of scraping the car on the ground, but problems with the suspension geometry, bottoming out etc. Also, if the free length required to achieve the ride height you want is too short, the spring could rattle around loosely when the wheel moves away from the car body (as when it drops into a pothole, or when facing the inside of a turn).
If you don't want to change your ride height, you MUST enter the same numbers you entered in the " Existing Suspension Design" section. You MUST also enter the outside diameter of your new tires, or the outside diameter of your old tires if you don't change them. Entering these numbers allows the spreadsheet to calculate the free length of new coil springs, based on not only the new spring rates, but also the new tires, new leverage and new car weights. Don't forget that the free length will be different for stiffer springs even if you want the same ride height -- because they will compress less under the same weight than the softer springs will do.
New Leverage
Changing wheels can change your leverages too. Enter the new numbers in here if you change wheels, otherwise you MUST enter the same numbers as before in these cells. The spreadsheet will then calculate the new leverages for both sway bars and springs. See the "Special Note..." for more details on special circumstances.
New Weights
If you remove any more sprung weight, enter the amount per end here (not per wheel). If you add weight, make the number negative -- to do so you should precede the number with a wordspace and a "-" sign. The change in weight resulting from new rims, lighter brakes etc. you can ignore because it is unsprung.
The Results
After you have entered values for all of the above parameters, the spreadsheet will automatically calculate the required wheel rates the new springs and sway bars should have in order to achieve the parameters you've decided on. You can then use the last section "New Suspension Component Design" to design new parts that will match the specifications called for in this section.
If you end up with negative wheel rates, which can happen with sway bars, you'll have to go back and change one or more of your parameters until all numbers are either "0" or higher. A negative number means that you're asking the impossible of your car. If you have to change any parameters it is best to start by changing the least important parameters first, like the favored speed. The total wheel rate ratio front/rear should be the last thing you compromise. You can use this technique of changing the parameters for other reasons too. For instance, if you don't want your car to use a front sway bar, you can keep changing your parameters until the spreadsheet reads "0" in the cell for the new front sway bar wheel rate. Don't go too far in changing your parameters, though -- it is easy to compromise them to the point where you might as well not use these spreadsheets. The whole point is to determine the OPTIMUM suspension for your car.
As mentioned before, this section is very similar to the first section so it doesn't require a lot of explanation. It is here to give you a workspace for determining how to design components which will result in a suspension that most closely matches the one recommended by the spreadsheet in the "New Suspension Design" section. You can also use it to examine the effects of substituting commercially available parts for the parts recommended in the last section -- parts that would often have to be custom-made to achieve the specific wheel rates recommended by the spreadsheet.
Chances are that you will merely re-enter a lot of the numbers from the first section into this section. What you will be doing is choosing a few key numbers to change -- like the wire diameters of the springs and sway bars. Keep trying new numbers until the spreadsheet displays a wheel rate value in the results cell that is as close as possible to the value recommended in the previous section for the same part. The spreadsheet then calculates a free length for the new coil springs, all the new wheel rates and ratios, natural frequencies and the new favored speed.
Ordering Or Building Custom Suspension Components
Ordering custom-fabricated suspension components is not as much of a problem as it might sound like. Most cities have shops that do a good, reasonably-priced job of fabricating springs and sway bars, or you can buy one of the sway bar kits available from companies like "Speedway Engineering" and build your own, or adapt parts meant for a different car.
If you order custom-fabricated springs, you should give the fabricator all the dimensions the new springs should have -- except the wire diameters or leaf thicknesses. Spring fabricators often use sophisticated alloys and heat-treatments to achieve specific spring rates, so the wire diameters or leaf thicknesses they choose might be different from those you'd expect. Just give them the spring rates you want the new springs to have. If you are ordering coil springs that have the end coils shaped differently to fit the spring seats, be sure to let the fabricator know what they are shaped like, and the dimensions of those end coils. This could include the "pitch" of them (the distance from one coil to the coil above it) and their inside diameter, if different. Tune to Win, by Carrol Smith has some good advice on this subject.
Some racers may wish to perform tuning methods not directly addressed in these spreadsheets, such as weight jacking, or designing trailer springs. Both can be performed rather easily and this section is meant as a guide to assist you in doing this.
Weight Jacking
Historically, this is a technique to achieve certain handling characteristics by either lengthening one spring, or shimming one end of a sway bar end link to place more weight on two wheels diagonally opposite each other on the car. In this section it is a technique to customize the ride heights and natural frequencies from side to side to compensate for the unequal weight distribution resulting in cars heavier on one side than the other -- such as when the driver sits on one side of the car. The problem is to design springs that are different from one side to the other, not just different from front to rear -- you end up designing four different springs. You will still want both front springs to have the same natural frequency and both rear springs to have the same natural frequency for optimum bump control. If the frequencies are different from side to side, you may end up with pitching in a sideways direction. This is what would happen if you used the same springs on both sides. Since one side would have more weight on it than the other, it would have a lower natural frequency than the other side would.
To do this, you'll have to measure ride heights and weights on each wheel (using wheel scales) with the driver seated in place. First, enter all the numbers for the side of the car the driver sits on in the spreadsheet, design your new suspension etc. until that spreadsheet is completely finished. Copy the spreadsheet and rename it so you know it's for the other side of the car and change the weights per wheel and the ride heights to those measured for that side. The spreadsheet will then design new spring rates that achieve the same natural frequency as those on the driver's side (and free lengths for coil springs) taking into account the different "corner" weights (ignore the sway bars, total wheel rates and total wheel rate ratios front/rear in the spreadsheet for the side the driver DOESN'T sit on). Sway bars make it impossible to achieve the same ratio of total wheel rates front to rear, on each side since they cannot be made in such a way as to have different rates on either side of the car. But the handling should be more nearly equal in both left and right turns using this technique since the springs are designed for the different loads they are subject to.
Weight Jacking For Circle-Track Cars
If you only have to make left turns it stands to reason that you can set up the suspension to favor left turns. Generally, this involves placing more of the car's weight on the left wheels to counteract the weight that gets transferred off of them and placed on the right wheels in left turns. Doing this results in more even loading of the tires in left turns. Often, the car is given a lower ride height on the left side as well since this causes the car to be more level while in left turns and also has the effect of transferring yet more weight to the left wheels.
Measure the weight on each wheel using wheel scales, with the car set up exactly the way you want to run it it, just as you would ordinarily do, or make adjustments to these weights based on what you want the new weight distribution to be. Making calculations based on these weights would favor bumps on the straights if the weight is measured with the car on level ground. If you want to favor bumps in the turns, you'll have to find a way of determining the weight distribution while in a turn. The amount the right side springs compress in a turn should give you the clue to find these numbers. Take some pictures of the car in a full-speed turn from head-on to measure the total compression of the right-side suspension. You can then calculate the approximate amount of additional weight transferred onto the right wheels by multiplying the total wheel rates of the right-side suspensions by the change in right-side ride height in a manner similar to that shown earlier -- but in reverse. The result is the total amount of additional weight transferred onto the right wheels. You can then change the car weights in the spreadsheet to reflect this weight distribution in turns by adding half of this weight to the existing weights on each right wheel and subtracting the same amount from each left wheel. If the track has banked turns, additional weight may be transferred onto the left wheels as well.
Now, enter the numbers for the right side of the car in the spreadsheet, design your new suspension etc. until that spreadsheet is completely finished. Then copy the spreadsheet, rename it so you know it's for the left side of the car and change all the numbers in it that are different for the left side of the car. This might include the different weight distribution, different ride heights and different tire sizes. The spreadsheet will then design new spring rates that have the same natural frequencies as those on the right side (and free lengths for coil springs) and take into account the different weights, ride heights and tires for each side (ignore the sway bars, total wheel rates and total wheel rate ratios front/rear in the spreadsheet for the left side).
Trailers
The problem with trailers is that it is impossible to tune their springs to work well in every given situation. One day your trailer may have a full load, the next it may be empty. Add to this the difficulty of dealing with leaf springs and it becomes very interesting. It is best to design them to favor the maximum load the trailer will carry. When measuring the weights, do so with the trailer loaded as you tow it. You may be better off if you weigh the trailer and the load placed on it separately.
If your trailer has only one axle, you don't have the natural frequency problems that a two axle car has. What you should do is match the natural frequency of the trailer's suspension to that of the rear axle of your tow vehicle. But when measuring the "wheelbase," measure the distance from the rear axle of your tow vehicle to the rear axle of your trailer. Then calculate the favored speed and the natural frequency of the rear suspension of your tow vehicle. Next, enter the tow vehicle's favored speed and different numbers for the trailer's "desired rear natural frequency" in the "New Suspension Design" section until "front" springs are displayed that have the same natural frequency as that of the rear suspension of your tow vehicle. The result is springs on the trailer that are matched to the tow vehicle at the tow vehicle's favored speed.
If you have a two axle trailer, do the same as above to calculate the frequency the front axle of the trailer should have, then calculate the rear trailer axle frequency based on the trailer wheelbase, just as above, but matching the rear trailer springs to the front trailer springs. Most trailers have axles that are very close together, though, so you may not have to even make that last calculation since the difference in recommended natural frequencies would probably be very small -- smaller than even the normal production
variations.
If you encounter a cell which refuses to display a value, make sure you have entered ALL the values required by the spreadsheet to calculate the result. Many calculations REQUIRE that a value be entered in all the cells pertaining to them, even if it is a random number, as is the case with the sway bar calculations, as well as some of the others.
Sometimes numbers refuse to display anyway. Some of the host programs won't display numbers above a certain size without you specifying this, so you should consult the manuals of the host program to determine how to make them display.
Another problem could be that you have deleted the equation in a cell normally used for displaying a result after unlocking the file. If this is what happened you'll have to copy your original spreadsheet and start over. That is why it is important to always keep backup files. Be very careful to only unlock the spreadsheet as long as necessary to enter your numbers, then lock it again.
Registered users ONLY may direct any questions about this manual or the spreadsheets to me by e-mailing me at dennisp@rahul.net
If you want to know more about suspension tuning, books like Tune to Win, by Carrol Smith and How to Make your Car Handle, by Fred Puhn are valuable guides. They deal with information that is well beyond the scope of this manual, like shock absorber adjustment, suspension geometry and detailed discussions on vehicle dynamics and testing.
© 1991 and 1995 Dennis Schøler Pedersen. This manual and all its contents are copyrighted. Any unauthorized copying or duplicating is forbidden by law. Authorization is given for registered users to print one copy of this manual per spreadsheet purchased.