Join Date: Jan 2013
Member # 236179
Location: New Iberia, La.
Might as well add the new Mark Ortiz Chassis Newsletter to the thread.
PROS AND CONS OF MID-ENGINE LAYOUT
The question sent to Mark.
Here is Marks answer:
Some clarity please.
The advent of the new C8 Corvette with its mid mounted engine inspires, again, some questionable comments on handling characteristics of such cars. To quote: “A mid-engine car has a low polar moment of inertia”, “allowing the car to change direction more easily”, but “it can be harder for a novice to recover should the tail break loose”.
The third quote seems problematic or unclear. It would seem that the low moment of inertia, and relatively high ratio of wheel torques to inertia, that enable the mid-engine car to change direction easily should also allow control to be regained more easily in a skid. Is this reasoning flawed?
Does the qualification of “novice” here have some relevance? Would a pro not have the same problem? The central driver location would reduce the driver lateral motion in a skid relative to a more rearward location, so that inertial information of a skid might be reduced, but the visual and inertial cues from rotation should be the same. Does the “harder to recover” statement agree with reality?
The polar moment of inertia referred to here is a measure of the car’s rotational inertia about a vertical (z) axis. This is expressed mathematically as the radius of gyration, conventionally designated k, or kz, times the car’s mass. To understand what the radius of gyration is, imagine that all the car’s mass was concentrated at one infinitely dense point, some distance from the center of rotation we are considering. How far away would that notional single mass need to be, to have the same rotational inertia as the car has? Stated another way, the car’s mass, times the radius of gyration squared, times rotational acceleration, equals rotational inertia.
Note that the radius of gyration is squared here. If the radius of gyration is twice as big, that means the mass accelerates linearly twice as fast for a given rotational acceleration, and also the resulting inertial reaction acts at twice the radius, so the rotational inertia is four times as great. The implication for the car designer is that relatively small changes in the radius of gyration have relatively big effects on car behavior.
Accordingly, for a given rotational moment applied by the tires (or anything else), rotational acceleration is inversely proportional to the square of the radius of gyration. When we reduce the radius of gyration, the car accelerates faster rotationally with a given excitation. So it is correct that a car with its masses centralized changes direction more readily. Or, more precisely, it changes yaw velocity (as distinct from yaw displacement) more readily. It starts rotating in yaw more readily, and it also stops or reverses yaw rotation more readily.
This is particularly useful for chicanes, slaloms, and any opposite-direction turns in quick succession.
The car actually has three polar moments of inertia, and three corresponding radii of gyration, for roll (kx), pitch (ky), and yaw (kz).
When we locate masses closer to the relevant axis of rotation, along either of the other two axes, we reduce the rotational inertia about the axis of rotation. For yaw, we reduce the polar moment of inertia by locating masses closer to the middle of the car, either longitudinally or transversely. The question of engine location mainly relates to longitudinal location of a major mass, but it’s worth noting in passing that moving things in laterally has some effect as well.
For example, the Lancia D50 F1 car of 1954 had outrigger fuel tanks between the front and rear wheels, hung out on struts from the body. These were intended to act as a form of fairing between the wheels, and to also provide fuel storage in a location where fuel burnoff would have less effect on weight distribution than with a tank in the tail. There was also some fuel carried in the tail, along with the oil. In 1955, the car was taken over by Ferrari and ran as the Lancia-Ferrari. Ferrari experimented with side tanks further in from the wheels, which reduced the yaw inertia. The first version with the tanks moved in retained fairings between the wheels but had the gap to the body filled in, and the tanks moved into that area. On the final version of the car, in 1958, the pontoons disappeared entirely, and there were smaller side tanks within a conventional-looking body. The reduction in tank capacity accompanied a switch from alcohol fuel to gasoline due to a rules change that year.
Such a change would also reduce roll inertia. This is less important, but it illustrates the point that moving a mass toward the center along one axis always reduces rotational inertia about the other two axes, not just one.
Correspondingly, moving the engine toward the middle of the car along the x axis reduces rotational inertia about both the y and z axes: in pitch as well as yaw.
This has implications for ride quality. It affects what ride engineers call the k2/ab ratio. (Note again the squaring of the k term.) This parameter comes from Maurice Olley’s work for GM in the 1930’s. In this expression, k is ky, the radius of gyration in pitch, for just the sprung mass. a is the horizontal distance from the sprung mass c.g. to the front axle. b is the horizontal distance from the sprung mass c.g. to the rear axle. For best ride, especially in lightly damped passenger cars, we want a k2/ab ratio close to 1. Or at least that works best assuming we’re holding wheelbase constant.
Olley arrived at this conclusion through experiments that involved a 1930’s passenger car with a k2/ab ratio considerably less than 1 due to the wheels being toward the ends. Olley hung movable weights off the front and rear of the car to make the k2/ab ratio adjustable. He found that if the car was really “end heavy” it tended to oscillate in pitch, a bit like a front end loader on soft tires. If the car was really “center heavy” instead, it felt stiffer, and thus harsher, in pitch. We should note that this relates to the car’s response to a pitch excitation consisting of sequential excitations at the front and rear axle, as when negotiating a speed bump or raised railroad crossing. The k2/ab ratio does not affect pitch displacement in response to braking or power application.
Anyway, a mid-engine car tends to have a “pitchier” ride over single-axle disturbances than one with the engine located closer to an axle. For sports cars, however, the central driver position makes pitch somewhat less noticeable to the driver, compared to a seating position close to the rear axle.
“Can be harder for a novice to recover should the tail break loose” pretty much does agree with reality, but the matter is a bit complicated. Partly, it depends on what we use to measure difficulty. In many cases, the required countersteer input may be smaller in magnitude, but it generally needs to come quicker, and it also needs to be taken back out quicker as the tail grabs again and yaw acceleration reverses. The usual problem in catching a slide is correcting too late, rather than too little, and often trying to compensate for lateness by overcorrecting. If the required correction needs to be prompter and also more delicate, that calls for greater quickness and finesse from the driver. Experience and training help with this.
Driver positioning is a factor, as well. Being seated close to the rear axle definitely does help you feel what’s going on at the rear contact patches, and you can still feel the fronts through the steering. Being in the middle of the car has its advantages too, though. Usually, it's easier to see, at least to the front. As already mentioned, it’s best for ride comfort, and it also makes the car feel more like an extension of your body. A rearward seating position produces more of a sensation of the car being a separate entity that’s dragging you around by the ankles. That isn’t really an impediment to driving the car, however.
For most road courses, really small yaw inertia isn’t a huge advantage. For open road races, as held in continental Europe and Latin America up through the 1950’s, it can even be desirable to have greater yaw inertia. This is particularly helpful when we may unexpectedly encounter small slippery patches, such as sand washes across turns or oily patches. The car does a smaller wiggle in such situations if it has a lot of yaw inertia. That in turn means the driver can drive a bit closer to the limit of adhesion for a given level of risk. So the designers back then weren’t necessarily wrong to build cars with front engines and transaxles in back, and say that the resulting yaw inertia was good thing.
In a mid-engined car, we can address this by making the wheelbase longer, and by setting the car up with a bit more understeer. The wheelbase tends to grow some anyway, when we move components inside the wheelbase and have to find room for them there.
Although we can’t really say that a car has a natural frequency in yaw, anecdotally it does seem that esses of particular frequencies tend to excite certain cars at yaw frequencies that create something akin to a resonant response and can cause loss of control in cars with large kz. There is a track near me that has what some people call the “Corvette trap” for this reason. Chances are that the C8 will not have the same problem, at least at that place on that track.
While much discussion of the rear mid engine layout focuses on yaw inertia, its most compelling advantages probably lie elsewhere. Assuming we’re using a large engine, and assuming we’ve chosen to drive only the rear wheels, putting the engine directly behind the driver gets us better propulsive traction and better braking than putting it in front, and hanging the engine behind the rear axle isn’t a viable option if it’s really big. Putting the engine behind the driver also lets us lower the driver’s eye level and hence the roofline and the nose, improving aerodynamics.