Basic Automobiles

Introduction

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This document attempts to describe everyday use of an automobile. The class of automobile considered is an average performance, front-wheel drive consumer vehicle.

Accelerator

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The accelerator, also known as the gas pedal controls the engine output. Pressing the accelerator increases the revolutions of the engine, mainly by allowing more air to enter the combustion chambers, or the cylinders, per revolution. The revolutions for various stages in this section depend on the engine, and every engine has a unique set of values. The tachometer gives the value of engine speed at any time. However, an experienced driver is supposed to know the speed of the engine without taking eyes off the road. When the car is first started, the engine moves at a speed called the idle speed. Many consumer cars provide means of changing the idle speed of the engine.

Say the idle speed of an engine is 1000 rpm (revolutions per minute). There is a minimum speed below which the engine will not fire, called the stall speed, and would be about 750 rpm for our engine. The other bounding value for the engine speed is called the red line. This is the maximum speed at which the engine can safely operate. For our engine, it is about 7000 rpm. Thus, it is the job of the driver to make sure that the engine speed stays between the stall speed and the red line. Moreover, the accelerator plays a very important role in the over all working of the engine thereby controlling the intake of the air inside the cylinder.

Steering

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Almost all the vehicles on the road today have some sort of steering wheel which is used to turn the tires. Typically, a rack and pinion mechanism is used which will turn the tires by a few degrees for several rotations of the steering wheel. Some vehicles have a dead zone at the center of the rack, so that you don't have to constantly adjust the steering while driving on the highway.

In the normal position, both hands should be on the wheel in the 10-2 position. To make a turn in a vehicle, rotate the steering wheel at the start of the turn. To make a turn to the left while moving forward, move your left hand to the top of the wheel, and pull down to the left. At the same time, let the wheel run through your right hand. As you near the end of the turn, steady the vehicle by moving your right hand to the top of the wheel and pulling down and right. Do not allow the wheel to spin back on its own! Even though this is very tempting, if you do, you will very likely lose control of the vehicle. You should have the wheels straightened when the turn is complete, or the vehicle will travel in an S shape, which is bad form.

Most consumer vehicles are understeered, as it is easier to handle for novices and unskilled drivers. Also, it is difficult to achieve neutral or oversteer in front wheel drive vehicles.

Power Steering

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Most modern vehicles marketed towards the average consumer has some sort of power steering installed. This means that the actual task of turning the wheels is performed by indirect means. Power steering is not preferred in racing cars as they reduce road feedback. However, it is much appreciated by the general public, especially for low speed maneuvers. New technology has come up with a very good solution--the speed sensitive power steering. This kind of power steering gives effortless low speed maneuvers, but firms up at higher speeds so that you can judge the grip of the tires accurately.

In general, there are two kinds of power steerings available--hydraulic power steering and electronic power steering. Electronic power steering is the more advanced of the two and is found in more advanced/modern vehicles. However, the feedback in hydraulic power steering is much better, so that driving is much more fun compared to a car with electronic power steering.

Turning Radius and Maneuverability

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The turning radius of a vehicle is the radius of the smallest circle in which it can turn. Two different values are given--the often quoted value is the curb turning radius, which is half the width of a road in which you can make a smooth turn without hitting the curb. The other value is called wall to wall turning radius, which is half the distance between parallel walls where the vehicle can turn.

The turning radius of a vehicle depends mainly on the wheel base and the wheel cut of the vehicle. Wheel base is the distance between the front and the rear axle. Wheel cut is the maximum angle through which the tires turn when the steering is rotated from the center. The smaller the wheel base, the smaller the turning radius, while smaller the wheel cut, the larger the turning radius. It may seem that a larger wheel cut is preferable. However, a larger wheel rotation will lead to more side forces on the tires, which might damage them.

Note that when a vehicle turns, the front wheels will have to turn by different angles so that there is no slippage. In a turn, the inner front wheel will have a larger cut. This is achieved by a mechanism known as Ackerman linkage. One of the modifications that you can make on a stock vehicle is increasing the wheel cut.

Given the front and rear overhang, the wheel base, and the wheel cut, we can calculate the wall to wall turning radius for low speed maneuvers for a vehicle.

The turning radius is related to the maneuverability of the vehicle, and also affects the design of parking spaces and driveways. What complicates the design is that the radius of the vehicle's travel varies continuously. Commercial software is available for such applications, but it takes a very simplified view--i.e., that the radius is constant, and equal to the turning radius. While this may enable us to see the absolute minimum space, the assumption is that either the driver stops the vehicle completely before making the turn (a very difficult maneuver without power steering), or that the steering is rotated extremely rapidly. What is more natural is that the vehicle is steered slightly at higher speeds, and more rotation is applied as the speed reduces, with the turning radius being achieved about 20% into the turn. Similar conditions apply to exiting the turn.

Aerodynamic Forces and Stability

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Modern automobiles travel at high speeds on flat roads, and this leads to large aerodynamic forces acting on the vehicle. The streamlined, close to airfoil nature of many vehicles lead to a large amount of lift even at moderate speeds. Many sports cars attempt to reduce the lift problem by having rear spoilers. Some of the higher end (though not the highest) cars attempt to provide more downward force using a rear wing. Note that such tricks increase the drag and reduce the top speed of the car.

Racing vehicles have attempted to deal with instability by lowering the body so that air cannot get between the under body and the road. Non racing vehicles are also expected to handle certain amount of unevenness in their path, so that they have a large breakover angle. Another method employed is to use a pump to lower the pressure at the bottom of the car, reducing the lift. However, this is not very practical for a standard car.

Drag Coefficient

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The drag coefficient of a car gives an indication of how aerodynamic the car is. However, note that CD, the drag coefficient is defined as

 

where V is the air velocity of the car, and A is the frontal area. Thus, a small sports car will have much lower drag compared to a van for the same velocity. Modern automobiles quote a CD value of less than .35, but frontal area is what counts in this situation.

As can be seen from the above equation, the drag force is proportional to the square of the air speed. Thus the horsepower required to overcome drag force is proportional to the third power of the speed of the vehicle. The rolling resistance is approximately independent of the speed of the vehicle, so that the horsepower required to overcome rolling resistance is proportional to the speed of the vehicle (i.e. it increases linearly). Thus, it is easy to see why it most sports vehicles have top speeds around 200 mph--to have a 20 mph increase in top speed a vehicle with 400 HP engine would need an additional 130 HP!

Driving a Standard (or Manual) transmission

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Many high performance cars, like older (before 1990) sports cars have manual transmissions. Also, cars with very low power output have manual transmission. For the sports cars, the owners are interested in the highest possible performance, and automatic transmissions, which contain "slush boxes" are not acceptable. The really small cars produce so little power in their engines that they cannot afford to waste any in the automatic transmission. Even a very well designed automatic will have about 5% losses due to the torque converter. Also, automatic transmissions are relatively heavier and more expensive compared to equivalent manual transmissions. The really high performance sports car being sold today have the automatic manual transmissions, which have the best of both worlds.

Preparation

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Before driving the car, make sure that you are able to sit in a comfortable position. Adjust the rear view mirrors so that you have a good field of vision. Depress the various pedals to make sure that you are comfortable with the operations necessary for driving the vehicle.

Starting From Rest

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Many manual transmissions have a hand brake (also called parking brake). When parked, they are secured by pressing the button and pulling the parking brake upwards until enough pressure is applied to secure the vehicle.

If the vehicle is on a level road, starting is quite straightforward. Place your right leg above the brake pedal and press down just to be safe. You will have to apply a relatively large force because the power brakes depend on engine vacuum to work. Put the vehicle in neutral gear by depressing the clutch and moving the lever down to the neutral position. For a modern vehicle, you can start by turning the key, which will start the engine at idle speed. For older vehicles, you may need to depress the gas pedal when you start. For both cases, after the engine has started, slightly depress the gas pedal to increase engine speed and hold it there. Some sports cars such as the Porsche Carrera GT have variable idle speed, so that the idle speed increases as the clutch engages, which means that you can start the engine without depressing the accelerator at all. You should not race the engine, as it will cause a lot of damage, the only resistance to increase in the engine speed is the inertia of the small fly wheel. Release the clutch to the bite point, where the vehicle starts to move slightly forward. After this, release the clutch slowly and smoothly and this will move the vehicle forward. After the clutch has engaged fully, remove foot from the clutch. You should never drive the vehicle with foot resting on the clutch. Depress the accelerator some more to increase speed.

Follow the same procedure, but with the reverse gear instead of the first gear for moving backwards from rest. Note however, that you will not be running with the clutch fully engaged in most cases since the speed will be too high for basic maneuvers.

Starting on an Incline

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Many times, you may be forced to park on a hill or incline. In this case, it is important that you be able to start the vehicle without it going backward, and potentially hitting someone behind you. There is a good way and two bad ways to do this.

The first bad way is to use the handbrake to hold the car while you put your foot on the accelerator and the clutch pedal. Now press the accelerator slightly and hold it there, so that the engine is at a speed somewhat higher than idle speed. Release the clutch till it reaches bite point, and as you feel the car starting to move forward, release the handbrake. This still requires considerable skill, as the engine will stall if you don't release the handbrake in time. Further, it will not work in cars which don't have a handbrake (many manual transmissions don't).

The second bad way is to put the vehicle in first gear and engaging the clutch fast enough while depressing the accelerator. The vehicle might not even move back if you do it fast enough. This can be done in places where you don't have any vehicles right behind you, and even if the vehicle moves back a little, you don't cause any damage.

The good way to start a vehicle on an incline is to hold the vehicle on the incline using the foot brake and slowly release the clutch. When you feel the clutch reach the bite point, remove the foot quickly from the brake and depress the accelerator slightly. Note that if you engage the clutch fully, or very close to that, the engine will stall as it tries to work against the slope and the foot brake. So the ideal point for releasing the brake is at a very small point before the bite point. Now, the engine is at its idle speed, and cannot pull the vehicle up the slope if the clutch is engaged. Even if you engage the clutch slowly at this point, the engine will stall. You will have to depress the accelerator so that the engine speed (and the torque) increases. Now release the clutch smoothly, while releasing the accelerator slightly. If you release the clutch and don't release the accelerator, the vehicle will move forward with a larger speed than you want. If you have done everything right, the vehicle will move forward, and this works in all situations. The usual mistake in this procedure comes from the inability to judge the bite point. On level ground, you can feel the vehicle start to move forward when the clutch starts to engage. However, on the slope, this effect is quite subtle and is easily missed, as the brake prevents the vehicle from moving. If you release the clutch too much, the engine will stall. In that case, depress the clutch, shift to neutral and start the engine again. However, if you don't release the clutch enough when you remove your foot from the brake, then you will be in a lot of trouble. If the clutch has made some contact, then you can depress the accelerator a lot to increase the torque, and move the vehicle forward. However, note that when you do this, you will have to release the accelerator fast as the clutch engages or the vehicle will shoot forward. Also, when you engage the clutch at such high speeds and torques, there is a lot of wear. If you release the accelerator too much, the engine will stall. The other possibility is that the clutch hasn't engaged at all when you remove your foot from the brake. This is the worst result possible, as the vehicle will now move backward, possibly colliding with the vehicle behind you. In driving tests, the vehicle moving back is instant failure. Note that it is a very bad idea to hold the vehicle on an incline using the clutch, as it can cause rapid clutch wear.

Stopping a Vehicle

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Depress the brake slightly to slow the vehicle, and once a good amount of speed has been removed depress the clutch fully and apply brakes smoothly to stop the vehicle wherever you want. After the vehicle comes to a stop, put the vehicle in neutral without releasing the brake. Turn off the engine. Now depress the clutch and if it is a downhill slope put the vehicle in reverse. Otherwise, put it in first gear. Release the clutch, and only then release the brake. You can stop a vehicle from any gear, but remember not to run the vehicle with the clutch depressed for a long time as it can still cause clutch wear. If your vehicle has a handbrake, engage the hand brake now.

Shifting to Higher Gears

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Once you have successfully engaged the clutch in first gear, you should immediately increase speed and engage the second gear. You should never operate the vehicle only in the first gear. It is used for starting the movement of the car from a dead stop and low speeds under 15 mph constant speed. Also, never shift to first gear while the vehicle is moving. To engage the second gear, release the accelerator and depress the clutch fully.

If you don't depress the clutch fully, you won't be able to move the shift lever in well designed cars. In many cars, no such fool proof method exists and the result will most likely be a sickening grinding sound of your transmission falling apart.

Move the lever down smoothly to the center. It should automatically fall into the neutral position. Now move the lever to the left and then pull down. Release the clutch smoothly and after that is done, depress the accelerator to increase speed suitable for second gear.

Your aim is to operate the vehicle at the highest gear possible considering the state of the road and traffic. Thus you should shift to the third gear as soon as possible, and this is as soon as your vehicle speed reaches the minimum value at which it can be driven in the third gear without stalling. To shift into third gear, release the accelerator and depress the clutch fully. Move the shift lever up slightly, and it will fall into the neutral position. In most passenger cars you can now move the lever up from here to the third gear position.

However, some vehicles may have the neutral position midway between the first and third lever positions, so that you may need to move it slightly to the right to move it up to third. As you can imagine, it takes quite a lot of practice before you can shift to the third gear of such a vehicle, which makes it very difficult to drive. Hopefully, the market will eliminate such unfriendly designs.

For a vehicle which has six gears, however, the standard H is necessarily different. For instance, the typical BMW shift has the reverse in the leftmost top position, with nothing vertically down. The six forward gears are arranged opposite each other in pairs, with the neutral between third and fourth.

Now that you have moved the lever to the third gear position, release the clutch. Depress the accelerator to increase speed and move to the next higher gear.

Moving to fourth gear is straightforward in almost all vehicles (even in the difficult ones mentioned earlier). Remove your foot from the accelerator, and depress the clutch fully. Pull the shift lever all the way down and this will move it to the fourth gear position. Now release the clutch and place your foot on the accelerator and increase the speed by depressing the accelerator.

Most vehicles have five forward gears, and engaging the fifth gear (usually the overdrive gear) is not difficult. Remove your foot from the accelerator, and depress the clutch fully. Move the shift lever up from the fourth gear and it will fall into the neutral position. Now move it all the way to the right and move it up to the fifth gear position. Release the clutch and depress the accelerator to achieve the speed limit value for the road. Note that you should never skip a gear, in most situations. So what exactly happens when you carry out the instructions above? When you take your foot off the accelerator, the engine loses speed due to internal friction and tries to fall back into idle speed. By the time you complete the actions required to shift the gear position, the rpm of the engine has fallen a fair bit. This is good, because you need the engine rpm to decrease when you shift gears up. Thus, taking the foot of the accelerator for the duration achieves the ideal. This clears up the intent of the statement in the beginning of the paragraph. The idea is to reduce the engine rpm to an acceptable value while keeping the road speed up. The reduction in speed will not be possible with skipping gears on a level road. If you wait a long time, then the road speed will also decrease, so that it will not be greater than the minimum required for that gear. Thus, you cannot shift from third to fifth, say, under normal circumstances.

Shifting to Lower Gears

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The most fuel efficient setting to drive a vehicle is at the highest gear available. However, there are cases when you might shift to a lower gear. The most common is when you have to reduce speed due to road conditions or traffic. There are two common methods to shift down, and one is much simpler than the other.

The common way to downshift to reduce speed is as follows. Remove foot from the accelerator and apply brake so that the speed of the vehicle reduces. Now depress the clutch fully and continue applying brakes till the desired speed is reached. Now release the brake and move the lever to the gear position appropriate for the speed. Release clutch slowly. Depress accelerator and continue. For instance, if you see that the vehicle in front is temporarily slowing down, you might want to shift down one gear, say, from fifth to fourth. However, if there is a major obstruction in the road, you might want to slow down to walking speed, and this requires engaging the clutch when in second gear. Remember that unlike shifting up, you can choose whatever gear you want when downshifting depending on the vehicle speed, except the first. Choose the first gear only if you have come to a complete stop.

Double De-Clutching

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Note that when you need to move to a lower gear, you want the engine to spin at a higher rpm than it is doing while in the higher gear. But if you have read the explanation of up shifting in the previous section, you will see that the engine speed will fall when you remove your foot from the accelerator. Now if you engage the clutch, the car will jerk as the engine tries to pick up speed. This is very hard on the synchro and the engine. The standard way to deal with this is to depress the accelerator while engaging the clutch slowly. However, this causes excessive clutch wear. The other method, which requires some skill, is called double de-clutching.

In this method, you take the foot off the accelerator, and depress the clutch fully. Then move the lever into the neutral position and release the clutch. Now depress the accelerator for a very short duration, which can be safely done as the clutch is engaged. Now release the accelerator and depress the clutch. Move the lever to the next lower gear, and the clutch can be engaged smoothly. Notice that you will be using the brake to slow the vehicle down, and this method requires you to take your foot off the brake to press the accelerator for a while. If you are braking because of some traffic trouble or an obstruction on the road, you may not want to do this. Also, this causes a sudden change in the forces applied on the vehicle, and it can affect the contact between the tire and the surface. Ideally, all the actions in the vehicles must be smooth, and you should avoid sudden acceleration, braking, steering adjustment etc. One way to avoid taking your foot off the brake is the so called "heel and toe" method. In this method, you apply brakes to slow the car down, and then depress the accelerator with your heel while keeping your toe on the brake when the gear position is in neutral. As you can imagine, doing so without changing the pressure on the brake pedal requires a lot of practice, but once done right, it is the best method.

When to Downshift?

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While the primary reason for downshifting is to reduce speed, there are other situations where it is useful. You get higher torque in lower gears, and you may want to shift down when facing a hill, if you want to avoid a stall. Another is when you want to overtake a vehicle quickly. You can get much more power when overtaking in, say, the fourth gear rather than the fifth gear if the vehicle has a 5 speed transmission. However, remember that the engine will red line (above recommended "rotations per minute of the crankshaft" which is referred too as "RPM") at much lower speeds in lower gears.

Fuel Efficiency

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The manual transmission is very efficient in terms of power transfer in that it doesn't have the fixed 5% loss in automatics. However, another reason many prefer manual transmissions is that it places a lot of control in the hands of the driver. While climbing a hill, you use a lower gear, since it will have larger torque available. However, once at the top, you can shift to neutral and turn off the engine, and roll down the hill. At the foot of the hill, depending on the speed you can shift to the appropriate gear. Note that the above may not be possible on many modern computer controlled cars, where shutting off the engine may lead to damage many of the running parts, and locking of the steering wheel.

Power Band

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The power band is the range of engine rpm where it produces good power output and this is between the torque peak and the power peak. In fact, the whole purpose of the gear box is to make sure that the engine works inside the power band at all times. Consider a vehicle going up a hill--as it moves up from level ground, the slope will cause and increased load against which the wheels have to work. If the engine is already in the power band, the reduction in speed will increase the torque (as it is beyond the torque peak), and you won't have to shift down. On the other hand, if the engine is not in the power band, the uphill motion will cause the RPM and torque to fall, requiring a quick down shift. If you enter a slope with the engine already lugging (too slow (low rpm)for that gear), you may have to double de-clutch (modern cars have synchronisers in all gears for upshifts and downshifts except reverse) rapidly to a lower gear or a gear two positions lower. For instance, if you approach a hill at the lower limit of your fourth gear, shifting down to third may not help due to the loss of momentum due to the slope of the hill. You will need to double de-clutch into second gear and then accelerate into third.

Braking

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When you encounter an obstacle in the road and want to slow down, you will do so by first removing your foot from the accelerator and allowing the vehicle to slow down before applying the brake. It is a good idea to give the driver behind you a warning in this occasion by blipping the brake. After the vehicle has slowed down a bit (engine braking), apply brakes slowly to reduce speed, and then depress clutch fully and slow down further by braking smoothly. Now you can switch to the appropriate lower gear and remove your foot from the brake.

One place where need for braking is not so obvious is while coming down a speed breaker. If you don't break when the rear wheel moves down the speed breaker, the rear end of your car will strike the ground, especially if it has a large overhang at the rear. So the procedure should be--brake well before the obstacle to make sure that your front is clear of it as the nose dips due to braking, then move smoothly up, making sure you have enough momentum to carry you through (very bad idea to have to rev your engine on a slope), and then when the rear wheel comes off the obstacle reduce the speed even further by smooth braking.

Should you use engine braking? Well, engine braking still acts through the wheels, so there is no great improvement in road handling. However, if you are travelling downhill, engine braking is recommended (and is the preferred method) as using the brake pedal will cause overheating and failure of the brake pads. Another use for engine braking is if you need to come to a stop rapidly. That is, if you have a vehicle suddenly stop before you, or you have a pedestrian jump in front, and you must absolutely stop the vehicle. Here you can switch to the lower gear rapidly (say from the 5th to the 2nd), and use the engine for braking along with the brake pads. Thus, if you have mastered rapid downshifting, you can bring the car to a stop using this method by using all the gears from 5th down to 2nd, instead of skipping gears. This will definitely cause engine damage, but is preferable to loss of life (either to you or the other people on the road). The usual method to use engine braking is to switch to a lower gear for this purpose.

The stopping distance in braking is roughly proportional to the square of the speed of the vehicle. Thus, you will need twice the stopping distance at 40 mph compared to 30 mph. The stopping distance also depends on the road conditions (whether it is wet, the road is sealed) and the condition of the tires. It is very important that you maintain adequate distance between your vehicle and the vehicles in front of you as well as the vehicles behind you. You should reduce speed and increase the distance in wet conditions, for instance.

Engine Damage

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If you follow the safe and recommended practices while using your car, your engine will last a long time. Note that the engine should not be raced (high rpm at low loads) or loaded at low rpm. It is easy to get feedback on high rpm--the engine noise increases as speed increases. However, low rpm loading, where you open the throttle at high gear when the rpm is low, is not as easy to detect. If you find yourself depressing the accelerator pedal too much at high gear, shift down to a lower gear to bring the engine speed up. Always be aware of the speed of your vehicle as you drive, and as soon as it drops, shift the gear down, this might result in more gear shifts, and that is all the more reason to choose a vehicle with a good gear box.

You don't usually have much choice in the kind of roads that you drive on, but try to use level roads as far as possible. Also, make sure that your driveway is flat and if it is at a higher level than the road, then make sure that the incline is closer to the road than the final parking position. Remember the warning about low rpms and high loads. A sure fire way to severe engine damage is an inclined driveway, which you drive up everyday at low speeds.

If you look at the load on the bore due to the dynamics of the crank motion of the piston and crankshaft assembly you will find that force acts on one side of the cylinder. Now, a properly designed engine will have the combustion forces act in such a way as to cancel this effect.

Driving Test

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You will need a license to drive a vehicle in any country in the world. The specifics of tests will differ, but the general idea is to demonstrate your ability to handle the class of vehicle for which you are applying for a license. A commercial license (to drive trucks, say) will have much more stringent requirements compared to a consumer license (such as for automobiles). There might be additional restrictions too--for instance, in many countries you cannot obtain a license to drive a manual transmission if you take the test on an automatic. The test consists of a written exam to test your knowledge of rules specific to the country/area as well as general rules, and a hands on test where you drive the vehicle in traffic as well as some specific maneuvers that you are required to perform. Also, you might be asked to negotiate some configurations (like the standard 8). The maneuvers might include, among other, parallel parking, and starting on an incline.

Parallel Parking

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Parallel parking is used to park a car on the side of a road, between two parked vehicles.

 

Some of the newer cars (e.g. the Toyota Prius) have automatic parallel parking, where it is done by the onboard computer.

Driving Terrain and Obstructions

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When you come across a road with pot holes in it, apart from slowing down, make sure that only one wheel goes into the pothole. Of course, it would be even better if you could avoid it altogether, but sometimes that is not possible.

Sometimes you may have to stop at a speed breaker--a good idea would be to straddle your vehicle across it, if you cannot go past it altogether before stopping. When you start, you can engage the clutch without revving the engine and then use the momentum to carry you over the obstruction.

Sometimes you get into a hole which you cannot climb out of even with a lot of revving. In this case you should unload your passenger and rock your vehicle using the first and reverse gears in sequence, building up amplitude as you would do with a swing. Do not do this for more than a minute or two as you can easily damage the engine. If rocking fails, you can try jacking the vehicle up, and filling the hole with some material from the road.

Low End Performance

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Many cars are not driven on highways, but within the city. While automobile manufacturers like to quote highway fuel efficiency and performance for their cars, many vehicles will spend most of their fuel in the city. As was mentioned earlier, the key to fuel efficiency is to run the vehicle at as high a gear as possible without lugging. This can be done by extending the power band to the low rpm range. One way to do this is by way of an exhaust chamber tuned for low end performance. Using resonance, it is possible to reduce the back pressure from the exhaust gases, so that the breathing of the engine is better even at lower speeds.

A hot rod method to increase low end torque is to use a water spray to cool the exhaust, which will reduce its pressure, leading to better engine breathing. A big design issue is to prevent entry of moisture into the combustion chamber. This kind of mechanism was used in the earlier heavy transport aircraft during take off.

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