Sometimes the simplest, most innocuous question requires a complex and demanding explanation. Or not. For example, say a 7-year old asks, “Dad, where did I come from?” And after enduring a long, strained explanation about the birds and the bees, the child replies, “No, I mean what country!” Recently, a racer’s question regarding the selection of gear ratios led to this analysis of the engineering considerations. The answer really varies a lot, depending on every individual’s specific needs and resources, from the casual amateur autocrosser to professional road racers—or from stock front-drive sedans with few gearing options to V8-powered racers with quick-changetransmissions.
If you run the same course a lot, and your car is just the way you bought it, you’ve probably found that the gears don’t match the turn exits or the straights very well. Maybe second gear is too low and you have to shift right away into third, or perhaps that gear is too high and you don’t have enough torque. Or maybe right at the end of the straight you either have to over-rev the engine or upshift for just an instant beforebraking.
You have three options to improve the situation, although your paths can be limited by budget, available equipment, or the rules dictated by the sanctioning body. You can change tire diameter, but this usually has a minor effect on gear ratio and a major effect on handling and ride height. (Don’t forget that raising the car will also affect aerodynamics.) Your second option is to equip your car with a quick-change transmission with many ratios available in everygear.
As a bonus, this might make it possible for you to get by with just one differential ratio for most tracks. Finally, if there are few or no options for the transmission, then hopefully at least the final drive can be changed to suit different tracks. However, that will change the ratio in every gear by the same multiple, which will probably upset you in another corner. Like we said, the realities of the situation may limit which of these choices you can make. Many of us may be limited to only a change of the final drive gear or perhaps the choice between a few different transmission cogs. Still, there is alwayshope.
Economy vs. Power
The ideal production differential ratio—those gears found at the car’s drive wheels—for the street is as high as possible for fuel economy, with an increasing number of transmission ratios to get good acceleration from a dead stop. That’s why some manual boxes may now come with up to six speeds, with possibly the top ratio being an overdrive. But whether you’re a beginner or pro, the optimum solution for competition will always be the same:
First, identify the ratios that create the maximum area under your engine’s torque curve between minimum and maximum rpm in each acceleration segment or straight; and second, reduce the gear shifting workload on the driver. Gearing is usually about the last stage in race car setup, since it depends on all the corner exit speeds and straight-away top speeds, which depend on the final development of cornering power, braking and aerodynamics. Not only does gearing have little return influence on those factors, it’s one thing that’s relatively easy to adjust at the last minute—in race cars that have quick-change ratios.
It is possible to resolve the question of optimum gearing for each race track by guess and test—unless the course is new or can’t be pre-run, as in autocrossing, which we will consider in a separate sidebar. But with many ratios available in some of the racing transmissions that can be fitted to the big front-engine, rear-drive cars, the number of choices and cost of track time make it important to use some rational method. Let’s first look at the professional approach, and then reduce it to a practical level.
Professional Approach
Figure 1
The ideal starting information would be a recording of speeds all around each specific track for a similar vehicle. From these, all the minimum corner speeds and maximum straight speeds can be found. This is one of the most valuable justifications for electronic data acquisition systems—even the simplest ones with just a few channels.
Otherwise, the driver must observe all these straight-away rpm points, possibly by voice or video recorder. The minimum and maximum ranges of acceleration for each straight can then be plotted as a bar chart, as shown at the bottom of Figure 1. Assuming there won’t be any standing starts, these bars let you calculate the total engine rpm range that has to be considered. Sometimes there may be just two options, with the choices limited to a close-ratio or wide-ratio transmission.
The basic difference in applications is between drag racing, with its standing starts, and road racing, where minimum speeds are possibly around 40 mph. For good drag launches, you often want the lowest possible first gear ratio and carefully spaced steps from there. But for road racing, if there are no standing starts or pit stops, you can be less concerned with a low first gear and instead make it higher and possibly useable on the course. Therefore you want the ratios stepped from the slowest turn to the maximum straight-away speed. In either case, the factory will probably have made those ratio selections already, based on their knowledge of the engine torque curve. However, when ratios are to be selected to fit the torque of a modified engine, or to meet the requirements of a particular road racing course’s turn speeds, then it helps to have a wider selection.
For example, the familiar BorgWarner T10 four-speed transmission was bought out by Richmond Gear and is available through [Tex Racing](http://www.texracing.com/). It has eight possible gear ratio combinations. [Richmond Gear](http://www.richmondgear.com/) also bought the rights to the old Doug Nash five- and six-speed transmissions, which have at least eight ratio possibilities in every gear for an almost unlimited number of combinations.
However, they are a lot more expensive and therefore cost prohibitive for all but professional racers. At this point, the serious racer might take his dyno torque curve and use a computer to convert it to thrust at the rear wheels in each possible gear ratio, then plot it against speed along with the bar charts of track speed. This can be seen in the top of Figure 1. The numerical labels on these curves show the differential ratio multiplied by the transmission ratio in every possible ratio selection. You start by selecting the lowest useable gear that doesn’t go way over the wheelspin limit (as 6.87 obviously does), then run it up to its maximum speed in rpm (or the point at which its thrust intersects the next ratio curve), and then it is shifted down to another higher ratio. Visually you can see the issue on the chart.
If you have a five-speed box, then you want to select the five ratios that would give you the maximum area under their curves in the shaded area. If it were possible to have an unlimited number of gears, or a continuously variable transmission, then the rpm could remain at peak torque and the thrust available would be one smooth curve. These curves also illustrate why it’s so important to have a relatively flat engine torque curve over as broad an rpm range as possible. If engine torque falls off sharply, or has noticeable dips due to cam selection or intake ram tuning or exhaust tuning effects, then it will be more difficult to avoid drops in the thrust curve by using ratio selections. This process also shows how the common practice of rating engines by peak horsepower is relatively unimportant.
A Simpler Method
But there is a cheaper and simpler way to select ratios: using experience and experimentation, as shown in our Simpler Method Chart. Our example is going to only consider three gearing options, and we’re going to say that the track only has four major straights. Although this is a limited exercise, we can still study the compromises forever without reaching the optimum solution, which is why pros want a quick-change trans with many options in each gear.
Right away, you can see that the wide-ratio option is “overgeared” for this track’s top speed and also has a big rpm drop between second and third. (The faster you go, the closer you want your gear change ratios to be, but that’s another, more complex story.) The 3.07:1 differential with the close-ratio gearbox raises second gear so much that the engine will be “bogging” coming out of the slowest turns—and you don’t want to downshift into first. This gives us another reason to lower the 3.07:1 differential ratio. (Remember that lowering the ratio produces a higher number.)
To find the ideal selection, multiply the final drive ratio by the redline speed in fourth gear (152 mph) and divide that by the top track speed (140 mph). This would yield a theoretical 3.33—which is close enough to the nearest available final drive ratio of 3.36:1. Combining this 3.36:1 final drive with the close-ratio transmission will yield just one shift point in the first three straights, and two in the last and longest one. There’s an even simpler way to determine the correct gear ratios: Simply base your decision solely on driver feedback. Say that in most straights, or in the most important ones, you tend to be over-revving or have to upshift just before braking. In that case, what you might want to do is install a slightly higher differential ratio (or a lower number—see the semantics sidebar).
You could even calculate how much of a change would be ideal, if you knew how much you were over-revving. Say you were going 500 rpm over a 6000 rpm recommended limit. Then you would want a higher differential ratio that was 6000 divided by 6500, multiplied by your existing ratio. It doesn’t matter very much whether you go with a higher differential like this or to a lower differential and then upshift earlier—unless you can use your top gear, which will probably be direct (or 1:1), and will have slightly less driveline power loss. There are a couple of reasons to minimize the need for shifting, among them to reduce the workload on the driver and minimize the possibility of blowing a shift (and the accompanying wrong gear, wear and tear on parts, etc.).
Less shifting also avoids the tenth of a second or so of acceleration loss from shifting “downtime” between gears. But don’t let that overcome the acceleration value of more gears to keep the engine in its torque peak. The simple answer for selecting the best gear ratios is to find the ones that make the driver happy, partly by minimizing the number of shifts, but more importantly by minimizing the lap times.
Simple Method Chart
Here is a down-and-dirty way of picking the best gearing for a particular car from three choices: 3.07:1 final drive with a wide-ratio transmission, a 3.07:1 final drive with a close-ratio transmission, and a 3.36:1 final drive with a close-ratio transmission. Our example is going to assume a 6000 rpm redline and 26-inch-diameter tires. To find mph in gears, use this formula: (.003) x (rpm) x (tire diameter in inches)/(differential ratio) x (transmission ratio). This math produces the following equation: 468/(differential ratio) x (transmission ratio). (The .003 just converts inches and minutes to mph.) Plotting speed bars at redline in all four gears for our different ratios produces this spread.
Transmission Choices: Synchronizers vs. “Dogs”
All transmission gear pairs are always in mesh, but are only intermittently engaged with their shafts. Passenger car transmissions make this connection with friction surfaces which contact first, to match rotation speeds more smoothly.
In racing use, these synchronizers wear rapidly, or are prone to more instantaneous failure. In pure racing gearboxes, the gears are alternately connected to the mainshaft by stepped cogs, also known as “dogs,” which are designed to engage or grab the next gear very rapidly and firmly, an action too harsh for everyday driving. The undercut angle and corner radii of these dogs are carefully designed to catch without wearing and to lock together firmly as long as torque is being transmitted.
Many drivers who have these kinds of boxes either power shift without letting up on the throttle, or only use the clutch for standing starts. And unless they are very good at it, the dogs get ground round, and as a result either won’t go in, or stay in, gear.
Either type of synchronization is helped a great deal if the driver learns to match speeds between gears by modulating the throttle pedal—by a split-second letup during the upshift, or a slight blip during the downshift. Otherwise, the synchronizers or lugs may be rapidly worn or broken, requiring the driver to match speeds even more closely—or perhaps even hold the shift lever in gear.
Gear Teeth Choices
Passenger car transmissions use angle cut or “helical cut” transmission gear teeth to reduce noise, while differential gears feature “hypoid” cut teeth. (These kinds of gears are also used to lower the driveshaft centerline.) For increased strength and efficiency, however, race cars use only straight-cut “spur” gears, which primarily have rolling contact on their faces, instead of sliding contact.
Gearing for Autocross
Gear ratio selection is a whole lot easier when your speed range is much narrower and much lower. The minimum corner speed for an autocrosser probably isn’t a relevant selection criteria here, because with lots of excess power at lower speeds, you can’t use full power for much of the turn, and therefore gearing is relatively unimportant.
If you have a data acquisition system to record your speed history, then it’s also useful to record throttle position. Or, if you even have a single channel of data, just record your speed while you’re at wide open throttle. The speed signal could be run through a simple on/off switch on the throttle stop. Let’s say your total wide open throttle speed range is from 35 to 60 mph—typical values for the average autocross, no matter where it’s being held. Then it’s possible you could select a differential ratio that would place a single transmission gear ratio—no matter which one—to cover that range. As a result, you won’t have a shift point right in the middle of a straight.
Practical Exercise
Time to put away the slide rules and see how gear ratios affect lap times. Our subjects will be a pair of Grand American Rolex-class Porsche GT3 Cup cars from Team Sahlen, and the exercise will involve comparing two different gearboxes, a wide-ratio box and a close-ratio one. Our classroom is Watkins Glen International, and team driver Wayne Nonnamaker is today’s professor.
“Turn 5, the middle of the graph, represents exiting the laces of the Boot at Watkins Glen and heading toward the toe of the Boot,” our driver notes. The top two lines on the Pi Research data acquisition printout represent the rpm for the two cars. “The black line is the graph of the car with the tighter gears, and the red line is that of the longer gears,” he explains. “You can see that the tighter gearbox has to perform two shifts on the straight, while the longer gearbox only has one shift.” The middle two lines represent the speed in mph of the two cars, with black for the tighter box and pink for the longer gears. “The bottom line is the gap between the two cars,” Wayne notes. “You can see down the straight that there is a couple of tenths of a second gain once the power is put down. You can also see that the longer gearbox does catch up dramatically when the other box is shifted, but the gain back isn’t enough to make up for the loss from being out of the powerband.” At this track and with this application, the close-ratio box produces the faster laps, even though a little more shifting is required.
“Also keep in mind that the Porsche GT3 Cup is a somewhat peaky motor,” Wayne adds. “This means keeping it in the powerband is essential. If you have a more broad powerband, this isn’t as essential. So when looking at how close you want your gears, the width of your powerband is very key.” While the gear ratios are part of the story, how much abuse those units can take also needs to be considered. “In our Rolex cars, the transmissioncan be shifted as quickly as you can physically do it,” Wayne explains regarding their Porsche GT3 Cup cars. Their Grand-Am Cup Porsche 996 machines, while outwardly similar, need a slightly more delicate hand. “In the Grand-Am Cup cars, you have to wait a brief moment or you will grind the transmissionand rip up the box.” Wayne says looking at the particular car is important when discussing gear ratios. “So if you have a Ford Mustang with a broad powerband and a transmission that takes a moment to shift; it probably isn’t worth it to tighten up those ratios,” he adds. “However, if you are running an Integra Type R where your transmission shifts rather quickly and the band is very peaky, then it will likely be worth it to tighten up the ratios.”
