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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: email@example.com. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
CALCULATING RATE OF SPRINGS ACTING IN COMBINATION
How do you calculate the rate of two or more springs acting together?
First of all, it matters whether the springs are acting in parallel or in series. If we have two springs side by side and we apply force to both of them so that they both deflect equally, they are in parallel. If we have two coaxial coil springs, one inside the other as with a dual valve spring, they’re in parallel. If we have two coil springs stacked one on top of the other, they’re in series. With more than two springs, it is possible to have series-parallel arrangements.
If we have a moving element with a spring above it and a spring below it, and both springs are active, the springs are in parallel. Examples of this in vehicle suspensions would include the sliding pillars in Morgans, some motorcycle “springer” girder forks, and the roll springing in monoshock car suspensions.
In some cases, two springs can be either in series or in parallel, depending on what aspect of the system’s dynamics we’re considering. For example, every car suspension actually has at least two springs per wheel: the main ride spring and the tire. As far as the sprung mass is concerned, the springs are in series, with the unsprung mass situated between them. However, the ride spring and the tire act on the unsprung mass in parallel.
When two or more springs act in parallel, the rate of the combination is simply the sum of the individual rates. That is, if Ktotal is the rate of the combination of springs having rates K1, K2 … Kn, then
Ktotal = K1 + K2 + … + Kn (1)
When the springs act in series, the reciprocal of the rate of the combination is the sum of the reciprocals of the individual rates:
1/Ktotal = 1/K1 + 1/K2 + … + 1/Kn (2)
For two springs, solving for Ktotal we get
Ktotal = (K1 K2) / (K1 + K2) (3)
For three springs, we get
Ktotal = (K1 K2 K3) / (K1 K2 + K1 K3 + K2 K3) (4)
These equations work for English or SI units.
Unless we are trying to create a spreadsheet to automate the calculation, for three or more springs it’s usually simplest to just sum the reciprocals of the rates and then take the inverse of that.
It will be apparent that when springs act in parallel the rate of the combination is greater than the rate of any of the individual springs, and when springs act in series the rate of the combination is less than the rate of any of the individual springs.
If you don’t remember the equations or rules for springs in series, you can reason out what the combination would do. Just figure out what the deflection of each spring would be under a particular load, add the deflections, and divide that sum by the load.
For example, suppose we had a 100 lb/in spring, a 200 lb/in spring, and a 1000 lb/in spring acting in series. If we put a 100 lb load on that stack, the springs would deflect an inch, half an inch, and a tenth of an inch, for a total of 1.6 inches. The rate of the combination is then 100/1.6 or 62.5 lb/in.
Or, using Equation 4 above,
Ktotal = (100*200*1000) / (100*200 + 100*1000 + 200*1000)
= 20,000,000 / (20,000 + 100,000 + 200,000)
= 20,000,000 / 320,000
= 62.5 lb/in
Or, the reciprocals of the rates are .01, .005, and .001 in/lb. The sum of those is .016 in/lb. The inverse of that is 62.5 lb/in.
OUTLAW FIGURE 8 CARS
I recently had a student come to me in my office at UNC Charlotte and ask me for suggestions for the Outlaw Figure 8 racing car that he and his father run at Evergreen Speedway in Washington
state. I’d heard of Figure 8 racing before but hadn’t paid any attention to it for years, and had no idea what an “Extreme” or “Outlaw” Figure 8 car was.
For those who are similarly unfamiliar with this little corner of the motorsports world, Figure 8 racing is a variation on oval track racing, generally done on specially adapted oval tracks, usually pavement. Instead of going down the straightaways in the usual manner, the cars cut diagonally across the infield twice each lap, so that the track has a figure 8 shape, with a crossroad in the middle. There are no rules about who has right of way at the crossroad. There are no stop or yield signs. You just try not to crash.
One thing that makes it a bit easier is that the infield is generally completely paved, and you can go outside the marked edge lines to evade crossing traffic.
To see some video of this track and these cars, see https://www.youtube.com/watch?v=3REKvWbPPxE.
It is unlikely that this type of racing will ever be done at very many tracks, partly because the track has to have characteristics that many oval tracks don’t have. It needs to have a paved infield, with nothing or next to nothing in it. It is pretty common for infields to be paved, but usually they are paved because the pits are there, and often various buildings, fenced enclosures, pit walls, and so on are there. To run a Figure 8 race, most of that stuff has to be absent, and there has to be someplace else for the competitors to pit.
The track needs to be fairly flat. Tracks that are medium banked or high banked are generally not suitable because the straightaways will generally have considerable banking and it’s hard to get a reasonably smooth transition from those to the flat infield.
Far as I can determine, there is no national sanctioning body for these events, and no universal set of rules governing the cars. These are track rule cars: the rules are made by the officials for the particular track.
The rules at Evergreen are relatively open. There is no minimum weight, no displacement limit, no restrictions on bodywork. Any kind of transmission is allowed.
However, for some reason all the cars look pretty similar. They are basically bodied as Modifieds: open front wheels, front engine, bodywork from the firewall back that covers the inner half or so of each rear tire but lets the outer half hang out, and fairly stout side crash bars. Noses vary a lot. So do wings and spoilers. Practically all the cars have huge side plates at the outside edges of the rear of the body. Some cars have sidepods that look to be designed to create downforce.
There is no ground clearance rule. There is nothing about powered downforce or movable aerodynamic devices. There is nothing about engine location. You can use any kind of suspension.
So, there isn’t anything explicitly preventing you from building a sucker car with a rear engine, or a car with a passively movable or driver-controlled wing, or a car with more than four wheels.
On the opposite side of the country, New Smyrna Speedway in Florida has the NASCAR-style catchall: if we don’t explicitly say it’s permitted, it’s prohibited. They also have a minimum weight and a ground clearance rule. West coast rules are very open compared to that.
However, there is this in the Evergreen rules: “All rules are subject to the interpretation of track officials. Any equipment that the officials consider exotic or not in the interest, or intent of the rules will be considered not legal for competition.”
Therefore, although you could build something dramatically different that could dominate, if you are too obvious about it they probably won’t let you run at all. What’s allowed is as much a matter of show business psychology as anything else.
What could you do that would realistically be allowed? What could you have on the car that might not be allowed but could easily be removed if necessary without destroying the car’s competitiveness?
Big wings, sideplates, sidepods, and spoilers are evidently tolerated. These are powerful cars on short, flat tracks, so downforce is crucial and drag doesn’t matter much. There are no dimensional limitations on the cars. You can run wings that extend long distances ahead of and behind the axles. You can run sliding skirts. Anything visible that doesn’t cost a lot has a decent chance of being allowed; your competitors can do it too, so it won’t destroy the racing. It will just give you an edge until the others catch up. So I wouldn’t be shy about escalating the downforce arms race.
I’m not sure what sort of rear ends people run, but since the car has to turn both ways I’d definitely run a limited slip, not a spool. There would be a significant advantage there if the competition hasn’t figured that out already.
Independent suspension might be considered “exotic” and prohibited, or it might not. It does cost money, and you couldn’t easily remove it from the car. If you want to run a beam axle in back, it should have linkage that compensates for driveshaft torque, as detailed in some of my earlier material. When you only turn left, torque wedge helps the car on exit. In a right turn, it hurts. Therefore, when the car turns both ways, you want to eliminate torque wedge.
There would be a good case for beam axles at both ends. Camber control is good, cost is low, and the suspension can be soft in warp without any exotic diagonal interconnection. That would be useful for negotiating the transition from the straightaway to the infield.
If I were setting up a class and wanted to keep it interesting both from a technical standpoint and from the standpoint of preserving a show where the winner is not a foregone conclusion, I would try very permissive design rules, but with a penalty ballast rule: if you win, you get ballast added to your
car for the next race. If you win again, you get some more. This proceeds until you don’t win anymore. Once you’ve gone long enough without a win, you get some ballast off. This lets innovators be rewarded with success, and gives the spectators the chance of seeing something technically new and interesting at the track, without allowing some wizard to run everybody else off and dominate indefinitely.