Many motorists spend a great deal of time and money trying to improve their vehicle’s performance. Some would like to improve fuel consumption, while others are more concerned about acceleration or maximum speed. Sooner or later, their thoughts turn to a change in axle ratio, or even just a different wheel size.

These attempts are seldom successful because a modern vehicle is the result of a number of compromises, and one of these is the choice of gear ratios, in the gearbox and in the final drive unit. These ratios affect the acceleration, top speed and fuel consumption directly, so that the numbers are usually chosen only after a thorough study of the effect of various possible ratios on the performance of the vehicle, augmented by a great deal of road testing. This means that any gearing change you make often makes the vehicle perform worse rather than better.

For example, few people realise that there is only one combination of overall gear ratio (ie: gearbox ratio in use multiplied by final drive ratio), combined with one unique tyre diameter that will give a vehicle its highest possible maximum speed for the particular engine fitted to the particular body shape. This will be explained later, but let’s start by looking at how the various performance criteria are affected by the gear ratios.

As an illustration we’ll use three sets of graphs that use the same numbers on the axes, but each graph will highlight different aspects of the performance, to avoid confusion. In each case the horizontal axis shows the speed, while the vertical axis shows th percentage of maximum power.

**– Maximum speed**

The maximum speed occurs when no further acceleration takes place. This is the point where the resultant of all the forces acting on the car, parallel to the road, is zero. This means that the total forward thrust delivered by the engine to the road, via the driven wheels, is exactly balanced by the total resistance to forward motion.

The immediate implication is that any change in either the engine’s output or the total resistance to motion will affect the maximum speed. The practical effect is that the maximum speed is easily increased or diminished by changes in atmospheric pressure, temperature and moisture content, which affect the engine as well as the resistance to motion, which is one reason why no two magazines will record the same maximum speed for the same car. Furthermore, the road gradient also has a major effect on maximum speed, so that one should only compare maximum speeds if they have been measured on a level road.

The gear ratios play a role here, because they affect the thrust delivered to the driven wheels, which is known as the tractive effort. This can be calculated by multiplying the torque at the flywheel by the overall gear ratio, and then dividing the answer by the wheel radius in metres. In earlier days, when cars had three- or four-speed gearboxes, and top gear had a 1:1 ratio, the gearing was usually chosen to give the highest possible maximum speed in top gear. Curve A in Fig 1 shows the situation, because here the gearing is chosen so that the engine output curve crosses the total resistance curve at the point where the engine power is at maximum. This obviously gives the highest possible maximum speed, because any change in gearing will shift the whole engine output curve, including the maximum power point, to a new position, and this must result in it crossing the total drag curve at a point that implies a lower maximum speed.

This is illustrated by curves B and C on the graph, and it can be seen that a lower ratio (higher numerically) as well as a higher ratio (lower numerically) will both give a lower maximum speed. However, the introduction of five-speed gearboxes has resulted in designers having more leeway, so that a modern fourth-gear ratio often gives the same result as curve B, ie a lower maximum speed than the previous fourth gear, while a modern fifth gear gives the same results as curve C. The advantage of such an arrangement is that there is extra power available for acceleration in fourth gear, while making it possible to cruise in fifth gear at reduced engine revs.

Note that the extra power at any speed is the difference between the engine power and the resistance, as shown, for example, by the vertical line at 100 km/h. It is interesting to note that the mass of a vehicle does not have a major effect on the maximum speed, because the frictional component due to the mass is a small percentage of the total resistance. It’s also worth noting that a car can be accelerated, fairly slowly, from standstill to maximum speed in top gear only, provided you slip the clutch to get going, ie the various ratios in a gearbox are not necessary to achieve a high maximum speed.

**– Acceleration**

Mass, force and acceleration are irrevocably linked by means of Newton’s equation of motion (F = Ma), which states that a force F causes a mass M to accelerate with an acceleration a. If we rewrite this equation in the form a = F/M, then it can be seen that the acceleration of a vehicle depends directly on the force propelling it forward, ie the tractive effort, and inversely on the mass of the vehicle.

This means, for example, that if you double the tractive effort, the acceleration, measured in metres per second squared, will be a number twice as big as before. This means that the acceleration time, measured in seconds to a particular speed, will be halved.

On the other hand, if you double the vehicle mass, the acceleration will be halved, so that the acceleration times will be doubled.

The above paragraph shows that maximum acceleration depends on the highest possible tractive effort, which can only be arranged by means of a gearbox, because the torque delivery of an internal combustion engine is not constant, but varies with the engine speed as well as the degree of throttle opening.

The ideal gearbox is a device that multiplies the engine torque by the correct amount to supply maximum tractive effort to the road wheels at any chosen speed. This is always a compromise, because a ratio that supplies extra tractive effort will allow the engine to over-rev at higher speeds, which explains why there are five or six gear-sets in a modern gearbox. Needless to say, no gearbox can always be in the correct gear, but the modern continuously variable transmission (CVT) gearboxes are close to the ideal.

This situation can be explained by means of the power output curves in various gears, drawn against vehicle speed, as shown in Fig 2. If the engine revs in each gear are superimposed on to the vehicle speed, we can graph the power available in each gear, and if this is compared with the total resistance to motion, as in Fig 1, a vertical line at any speed will show the amount of power available. Note that it also shows the gaps in power delivery due to the fact that there are only five gears. This shows, in graphical form, the advantage of having more gears, and also why so much development work is going into CVT gearboxes. Note that the curve of maximum drag or resistance can also be labelled the cruising power curve, because at any constant speed the power developed by the engine is exactly equal to the total resistance, because no acceleration takes place. Interestingly enough, the torque converter found on virtually all automatic transmissions usually multiplies the engine torque by some factor, and so helps such a transmission to get away with one gear ratio less than a manual gearbox.

Another way of looking at a choice of gear ratios is to realise that maximum pulling power results from an engine always operating between the maximum torque revs and the maximum power revs. This also ensures good drivability, even at small throttle openings, because it means that the engine operates at a point on the torque curve that is past the maximum, so that any reduction in vehicle speed, for example when going up a slight incline, will result in an increase in torque, making gear-changing unnecessary.

To achieve this situation, the gear ratios are chosen in the manner shown in Fig 4. The gearbox output shaft speed is marked off on the horizontal axis, while the engine revs are marked off on the vertical axis. A horizontal line is drawn to represent the chosen maximum engine speed in top gear, followed by a vertical line to represent the maximum gearbox output shaft speed. Next, a straight line is drawn from the meeting point of these lines to the origin. This line will make it possible to read off the output shaft speed at any engine speed, in top gear, so this is called the top gear line.

To decide the intermediate ratios, a horizontal line is drawn across the graph area to represent the peak torque engine speed, followed by a vertical line through the point where this line crosses the top gear line. Once again we connect the meeting point of this line with the origin, because it will give us the third gear line; ie we are able to read off the relationship between engine speed and output shaft speed, in third gear, on this line. The remaining two gears can be found in a similar way, and the spacing will be such that each up-change will result in the same drop in engine revs, and at full throttle the engine will stay between the maximum power and maximum torque speed. The gear ratios will be in geometrical progression, ie each ratio divided by a higher one (lower number) will give the same answer.

This is known as perfect gearing, and was the norm in the days when cars had four-speed gearboxes, but most modern gearboxes have ratios that are modified versions of this arrangement, mainly because of the lower fourth and higher fifth gears that have been mentioned.

**– Fuel economy**

It’s obvious that a high overall gear ratio (low number) reduces engine speed at any particular vehicle speed, but the choice of ratio must be done scientifically, by studying all the factors involved, rather than using thumbsuck methods. A graph that shows the engine’s specific fuel consumption, superimposed on a power-against-engine-speed graph, is often used. his is called an engine map, and an example is shown in Fig 3.

The specific fuel consumption in g/kW hours, measured on an engine dynamometer, at a steady speed and a fixed throttle opening, is equal to the fuel consumption in g/hour divided by the kW developed by the engine, and is a measure of engine efficiency. This obviously varies with engine speed and throttle opening, and is normally the most favourable, ie has the lowest value, at large throttle openings and low engine speeds. The large throttle openings reduce the pumping losses, while the lower engine speeds reduce frictional losses inside the engine. On the particular graph shown, the most economical engine speed for a situation where the car needs 60 kW would be about 2 000 r/min, because the specific fuel consumption has its lowest value inside the ellipse that shows a value below 250 g/kW.hr.

** – Factors that influence resistance to motion**

Air resistance, the drag due to the resisting influence of the air, depends on the air density, the frontal area of the vehicle (ie the area you would see on a photograph taken directly from the front), a drag coefficient that depends on the shape of the body, and the square of the vehicle speed. The fact that vehicle speed has to be squared implies that the drag increases dramatically with vehicle speed. In fact, the drag at 200 km/h is four times the drag at 100 km/h.

Rolling resistance is the resistance to motion due to the tyres and the various bearings and gears in the transmission. It does not vary much with vehicle speed but increases slightly above 100 km/h due to tyre distortion. In fact, at 80 km/h the rolling resistance of a family saloon is about equal to the air resistance.

The gradient augments or reduces the level road tractive effort by a factor that is equal to the mass of the vehicle times the acceleration due to gravity (9,82 m/s) times the sine of the slope angle. This is easy to calculate on a scientific calculator; for example, if a car has a mass of 1 014 kg, and is going up a slope of 10 degrees, then the tractive effort is reduced by 1 014 x 9,82 x sin(10) = 1 729 newtons. On the other hand, if the car was going downhill, then the tractive effort would be increased by this amount.

**– Changing the tyre size**

The effect of a change in wheel size can only be calculated if you have a set of drag vs power or traction curves, which means that the ordinary motorist can only make an estimate of the change. This is done by looking at the percentage change in wheel diameter. For example, if you want to change from a 175/65 R14 tyre to a 185/65 R14 tyre, then you should consult a tyre dealer, who will be able to read from a tyre chart that the first tyre has a circumference of 1 780 mm, while the second tyre has a circumference of 1 820 mm. This means that the circum- ference of the second tyre is 40 mm or (40/1 780) x 100 = 2,2 per cent bigger, so that the acceleration should be approxi- mately 2,2 per cent worse, but the engine speed will be the same percentage lower at any speed, and the speedo will read the same percentage under. The effect on fuel consumption cannot be calculated in this manner, because the engine might now use more fuel, depending on how the change relates to an engine map.