Two Guys Rally

Combustion Engine Theory: Intro [ March 29th, 2009 ] By:Mark Ozimek

I was thinking the other day (rare, I know) it’s about time that I started up another interesting series. How about something that is at the heart and soul of almost every motorsport: The engine!

This is just the introduction to engines, I’ll cover the common terminology and give everyone a good starting point for understanding the finer design choices that I will cover later on.

Most automotive racing is powered by internal combustion engines. There are some variations within there to make things interesting. There are usually either two stroke or four stroke engines. I’m gonna focus on the latter, because two stroke engines are basically non-existent in rally. In four stroke engines, there are… wait for it… four strokes!

• Intake: The piston is moving downward, away from Top Dead Center (TDC) with the intake valve(s) open and the exhaust valve(s) closed. This draws in fresh air/fuel mixture to burn later.
• Compression: Intake valve closes, usually just after Bottom Dead Center (BDC), and the piston moves up to compress the air/fuel mix. Just before TDC (usually 10º-40º of crankshaft rotation), the combustion begins, either by igniting the fuel with a spark (gasoline) or injecting the fuel into the compressed air (diesel)
• Expansion: This is the stroke where the power comes from, the burning air/fuel mix generates a lot of heat and pressure that pushes the piston down, generating torque.
• Exhaust: Just before BDC, the exhaust valve opens up, and the piston moves back up to push all of the burnt gasses out of the engine. Once it reaches TDC, things start over again with the intake stroke.

The next choice is the type of fuel. Diesel engines run by compressing air a lot to generate very high temperatures, then inject the fuel, which combusts to generate pressure and heat that drives the engine. Spark ignition engines run a bunch of different fuels, usually gasoline, but can also include mixes of gasoline, ethanol, methanol, propane, compressed natural gas, and a few others. The air fuel mixture is ignited with a spark instead of relying on the sheer amount of heat in the diesel cycle.

There are also variations of the typical reciprocating piston engine, the most common being a rotary, or Wankel engine. The piston is replaced by a rotor with three faces housed inside of an oval-like housing that is technically known as an epitrochoid. Rotary engines have a very high power/displacement ratio because there are three power strokes for every revolution of the rotor, compared to the one power stroke every two revolutions of the crankshaft of a normal four stroke piston engine. However, sealing and lubricating the piston is a significant issue that hampers the reliability of this design

So now that this is out of the way, it’s time to get into the common terms used when describing or talking about engines. Let’s start at the macro level, things that everyone should be familiar with and move our way in.

Displacement: The amount of volume that all of the pistons displace in one stoke. This is dependent upon the number of cylinders, the bore and stroke.

Bore: The diameter of the cylinder when viewed from the top. The piston diameter is a small amount less than this, with rings to provide a good seal

Stroke: The distance the piston moves from TDC to BDC. This is dependent upon the crankshaft dimensions.

Compression Ratio: The ratio between the displaced volume (Vd) and the volume in the top of the cylinder (Vc) when the piston is at TDC. To calculate, CR = (Vd + Vc) / Vc.

Air/Fuel Ratio: Also known as AFR, or it’s reciprocal, FAR. Gasoline likes to burn within a specific range of ratios between the mass of air present and the mass of fuel present, typically between 8:1 to 20:1. the combustion can be considered the most “complete” when the AFR is stoichiometric (the wiki article does a better job explaining the chemistry than I ever could), 14.7:1 for pure gasoline, or ~14.2:1 for the 10% ethanol blend that almost all pump gas is now. This means that for every 14.7 kilograms of air that flows through the engine, the engine will try to supply 1 kg of gasoline. Ratios that are lower than stoich are called “rich”, and higher is “lean”. Given a constant set of parameters and optimized ignition advance, AFRs around 12.5-13 for gasoline give the most torque, because the fuel burns the fastest then.

Ignition Advance: Measured in the number of crankshaft degrees before the piston reaches TDC. Typically spark will be tuned to create maximum cylinder pressure around 14º after TDC. More advance is needed when the engine spins faster, because the burn speed of gasoline does not increase with the engine speed. However, the burn speed does increase with air density, and with AFR, with a maximum burn speed for gasoline being around 12.5-13. As such, timing is typically less advanced with more open throttle or higher boost pressure, but more advanced at higher engine speeds. Many design factors play a role in optimal ignition timing.

Volumetric Efficiency: This is essentially a measure of the amount of air that goes into a cylinder compared to how much a piston displaces. Since air is compressible, meaning the density changes with pressure, it makes more sense to think of it in terms of mass. A volumetric efficiency of 100% would imply that the mass of air that is in a piston is the same as the mass of whatever the displacement would weigh in the surrounding air. So taking the 100% efficiency example further, if it was a 4 cylinder 2.0L engine running at 100% efficiency at STP, the mass of air inside one cylinder would be equal to the density of air (1.184 kg/m³) multiplied by the volume (0.5L), the result is 0.592 grams of air. Doesn’t sound like a lot, but air is pretty light, and when you’re turning the engine at 6000 rpm, the engine is moving about 7 kg/min of air.

Mean Piston Speed: The average speed of the piston as it moves through a cycle. This is dependent upon the RPM (referred to as N in calculations) that the engine is running at and the stroke. To calculate, Sp = 2 * N * Stroke. Due to material strength and fatigue limitations, it is uncommon to see the mean piston speed exceed 25m/s or so, except in extremely high performance racing engines, like F1.

Brake Mean Effective Pressure: Commonly BMEP (or MEP when not measured at peak torque or power), this a way to measure how effective an engine is at making power in relation to it’s displacement and rpm. As a general rule of thumb, the more power you make per amount of displacement and the less rotational speed at that power level, the higher the BMEP is. Alternately, for those of you who know how torque, power and rpm relate to each other, the peak BMEP of the engine is at the peak torque of the engine. To calculate MEP, you need to know either the power and RPM, or torque, displacement, and number of strokes (2 or 4)

Calculating with power and rpm:

MEP = (P * Nr * C) / (Vd * N)

P is power, in HP or kW
Nr is the number of revolutions per power stroke, 1 for 2-stroke, or 2 for 4-stroke
C is a constant, use 396,000 for imperial (hp & ft-lbs) or 10³ for SI (kW & N-m)
Vd is displacement, cubic inches for imperial or liters for SI (61.02 CI per L if you need to convert)
N is the engine speed in RPM

Or with torque:

MEP = (T * C) / (Vd)

T is torque, ft-lbs or N-M
C is a constant, 75.4 for imperial, 6.28 for SI

Well, that’s it for the intro. I’m sure some of you have specific things that you would like me to go into detail on in this series, feel free to ask, and I’ll try my best to cover it!

How Engines Respond to Air Temperature [ April 24th, 2008 ] By:Mark Ozimek

I’m sure that everyone has heard or experienced first hand how cars have more power when it is colder outside. This may strike some of you as being counter-intuitive, but from a technical standpoint, it makes a lot of sense. Let’s break it down to see what is happening when it gets cold out.

The engines in cars burn gasoline (or diesel) and oxygen to create energy. The heat created by this explosion causes the air inside the cylinder to expand, pressing down on the piston, which creates a torque in the crankshaft. There is a very specific ratio between the amount of gasoline and air that provides peak power. This ratio is called the Air/Fuel Ratio or AFR, for obvious reasons. Get too far away from this ratio, and the gasoline won’t even ignite! As a general rule of thumb, engines run with around 12 to 16 pounds of air per pound of gasoline. Below 14.7:1 is called “rich”, while above that is “lean”, while 14.7:1 is “stoichiometric” for normal gasoline. Typically cars run lean for better economy when subjected to low load conditions, and rich when the pedal is to the floor, to help prevent overheating of the engine. Getting into optimal AFRs will be an article for another day though.

Why does all that matter? Well, notice that it is pounds of air and fuel. Engines have a constant volumetric displacement, but it’s possible to vary the mass of air flowing into the engine by changing the density of the air flowing into the engine. In fact, this is exactly how a throttle valve works. When the throttle is partially open, the air flow is restricted such that the density of air in the cylinders is very low, so there is very little mass. The ECU is aware of how much air is in there and injects an amount of fuel to match to get close to the AFR that it wants. A turbocharger or supercharger takes this in the opposite direction and increases the density of air by compressing it.

All of this has a point, don’t worry! Many of you have surely taken some sort of chemistry class, either in high school or college. To make things simple, air can be modeled as an “ideal gas”, which means we can easily say how four very important things relate as you change one of them: Density, Volume, Temperature and Pressure. The density and temperature terms are the critical ones for explaining why engines have more power when it is cold out. As temperature decreases, the density increases. That means when it is cold out, the engine will be able to contain a higher mass of air than at a higher ambient temperature, assuming the same throttle position and engine speed. When there is more air, there is more force from it’s expansion when the gasoline burns, which translates to more torque and power.

We can take this a bit further though. Notice the pressure term. At sea level, the air pressure is much higher than it will be somewhere like Independence Pass, Colorado, at 12,095ft. At this point, the pressure is down to about 60% of the pressure at sea level. Pressure and density have a direct relationship, so at 60% of sea level pressure, the engine is flowing 40% less mass, which will then correspond to a loss of about 40% of the engine’s power that it had at sea level (This is a rough approximation and it will be more or less depending on load and engine design. Having a turbocharger is a good way to get around this loss in pressure, but a significant power reduction will still be there). Pretty substantial, isn’t it? Now you know why the WRC racers were complaining about how slow the cars felt in Mexico, as they were racing at around 6,000ft for much of the course.

Another thing to note: With lower air temperatures, while the engine power increases due to the increased density, the drag from air resistance increases as well. The body of the car has to push more dense air out of the way as it is moving forward. This will negate a lot of the benefits of the extra power at higher speeds, but drag is a very minor part of the forces a car must overcome when accelerating at low speed. A similar effect is going on at high altitudes.

Ditch Gasoline?! [ April 14th, 2008 ] By:Mark Ozimek

So Charles and I were talking about the engines in rally cars the other day, specifically how the horsepower in the WRC is limited to 300hp. If you have read my article on engine power and torque, you’ll realize that this means they have the option to make amazing amounts of torque at lower rpm while staying under that 300hp limit. It is possible to design a gasoline engine to stay close to 300hp for a good part of the rpm band. Just size the turbo right so that there is a lot of boost down low and use a control system to taper off the boost in higher rpm to not exceed the power limits, coupled with a well-configured camshaft profile and such.

This type of power output curve very closely resembles that of an electric motor. The most torque is seen at or very close to 0 rpm, with the power output being pretty constant through the rpm range. This torque makes an electric motor great for starting off the line, or coming out of slow corners with lots of acceleration. There is another aspect of an electric motor that makes it far superior for the responsiveness that rally racing requires: the power response is instantaneous. With an internal combustion engine (abbreviated ICE), the throttle valve opens when you push the pedal down. This allows more air to flow into the engine, the ECU will see this through various monitoring methods and inject for fuel to keep the mixture close to what is required for the conditions (usually around 12:1 to 14:1). Then the exhaust gas flows through the turbine wheel, makes the turbine and compressor spin faster, increasing the pressure in the intake, causing even more air to enter the engine, creating more power. As you can see, there are quite a few steps involved here. The throttle response of a typical ICE is considered to be pretty fast, which is why they are used in cars, but in comparison, the electric motor is much must faster.

Simply press the accelerator pedal (not a throttle anymore!), the power control circuitry will allow more current to flow through the motor, and the motor creates more torque. No waiting for air to accelerate into the engine, no waiting for the ECU to compensate for this extra air with more fuel, no waiting for the exhaust to flow past the turbine to spool it up. It’s nearly instantaneous in comparison.

There are quite a few other advantages to electric motors aside from this. The thermal efficiency is often >80%, while a typical high performance ICE will be lucky to get 15% efficiency out of the gasoline it burns. The overall package size and weight of the engine itself is greatly in favor of the electric motor. Same with reliability: a gasoline engine has a lot of moving parts from the crankshaft up to the valvetrain, while an electric motor just has the core that spins.

The two of us sat there and discussed this topic for quite a while, and realized how amazing it would be. There is just one significant technical hurdle left to overcome: the batteries. Getting the range and power output needed for a rally car will weigh a lot. However, it is definitely something to consider as a possibility for the future of rally racing. What do you think about it? What other unforeseen problems do you think there would be? We would really like to hear what you think.

Engine performance: Torque and Horsepower [ April 8th, 2008 ] By:Mark Ozimek

Time and time again, I see people all over arguing the endless debate in engine design: Torque vs Horsepower, and which one is better. Although I am aware that ending this debate is impossible, and trying to do so would be quite insane, I wish to share what the engineer in me thinks matters most.

A quick crash course in physics for those who are not familiar with the topic. There is a very simple relationship between acceleration, mass and Force: F=m*a. Bear with me here, we have a lot of fun material to cover.

For cars, the force that causes the car to accelerate and decelerate (braking!) is generated by the tires and the ground. There is a torque at the wheels that causes the wheels to rotate. The fricton between the tire and the ground converts this torque into a force. This force is equal to the torque applied to the wheels divided by the radius of the wheel, with this radius measured from the center to the tire’s contact surface with the ground. This is assuming that the tire is not slipping. If it is slipping, then the force is dependant upon a lot of other things, like the surface conditions, friction coefficient, how fast the surface of the tire is sliding across the ground, temperature, and a few others.

With our intentions of rally racing, we obviously want the most acceleration possible to get out of slow corners quickly, while still having a fairly fast top speed for the straighter sections of the course. We can rewrite the relationship given above to be a = F/m, which implies that either increasing the Force or decreasing the mass will improve the acceleration of the car. The mass would simply be the mass of the car, more commonly refered to as the weight. I won’t get into how this affects acceleration yet, since this is an article on the engine, not weight reduction.

Now since more force determines acceleration, and the force increases with more torque, you’re most likely thinking: “AHA! So torque really does detemine the acceleration of the vehicle”. You are correct to think this, but there is a catch: it’s the torque at the wheels that matters. Taking it a step further, it is the engine torque and overall gear ratio that determines the torque at the wheels. This may seem obvious, but this is why acceleration is greater in 1st gear than a higher gear, such as 2nd or 4th. The gear ratio is much higher in lower gears, causing the torque that the engine generates to be multiplied by a factor of 8-15 in first down to around 1.5-3 in fifth gear, depending on the gearbox setup.

The consequence of this is that the output rpm from the transmission is much lower in the lower gears, so it is difficult to reach high speeds in low gears unless you’re using an F1 engine that hits the rev limiter at 19,000rpm. So now we have three factors to consider, the torque the engine is creating, the gear that the car is in, and the engine speed, to determine the acceleration of the car and the speed that it is traveling at.

So where does horsepower come into play? It’s quite simple actually. Using the imperial system, horsepower, torque and engine rpm can be related very simply: HP = (torque * rpm) / 5252. That bottom number is just the combination of factors used in unit conversion, since HP is a measure of power (who would have thought?!) which is an amount of work done per unit time. As a visual representation of the relationship between these three things, consider two power sources that I will use in an example later: One that puts out a constant amount of power, and one that puts out a constant amount of torque.

Realistically, an engine’s power and torque curves will look more like this, for a well configured turbocharged engine:

Work and torque are the same thing, in a twisted sense. Work is measured by a force applied over a certain distance. Pounds is a force and a foot is distance. Say you pressed on a block with 200 lbs of force over a distance of one foot. You just did 200 ft-lb of work.

To convert it into power, the time it took to do this amount of work is needed. Let’s assume that you’re a strong guy, and managed to do 200 ft-lb of work in just a half second. This means that you generated 400 ft-lb/s of power. Way back in the day, it was decided that there are 550 ft-lb/s of power in one horsepower. This means that you just generated 0.72hp when you moved that object in a half second.

To clarify power further, consider two different power sources, a turbocharged gasoline engine and an electric motor. The gasoline engine puts out a constant amount of torque through a broad rpm range (not really, but go with it for simplification of the explanation), while an electric engine puts out a pretty constant amount of horsepower, but has a very high RPM limit. To achieve the same range in speed, the turbocharged gasoline engine needs a gearbox to vary the ratio between the engine speed and wheel speed. The electric motor does not need this gearbox, as it has lots of torque at 0 rpm and can spin much faster. The electric motor will have a pretty smooth acceleration curve. The most acceleration will be seen when starting from a stop, due to the high torque at low rpm. As speed increases, the accleration tapers off because the motor creates a constant power; at high rpm, the torque is very low. On the other hand, the gasoline engine will produce an acceleration curve that looks like a step function. It generates a consistent amount of torque through the usable rpm range. As a result the acceleration in each gear is roughly constant while speeding up. When the driver shifts to a higher gear as the speed increases, the amount of torque to the wheels drops, thus decreasing the acceleration of the car.

How does all this fancy unit conversion relate to the rally car? Well, while the torque gets multiplied and changed along with the rpm through the transmission’s gear ratios, the power stays the same, minus some losses through friction, regardless of the gear. This power that the engine puts out can be directly equated to the power put into accelerating the car, overcoming the various drag forces, moving the entire car up and down hills, and so forth. This is where I introduce another equation, one that relates Energy with mass and velocity: E = (1/2)*m*v²

To avoid getting into calculus and integrating power with respect to time, just keep in mind that energy can be thought of as the total amount of power that has been applied to the system, which in this case, is the car. The more power the engine generates, the faster the velocity changes. The change in velocity is measured as… dundunDUN! The acceleration! However, note that the velocity term is squared. As the speed increases, the engine needs to create more and more power to maintain the same accleration. This should sound pretty familiar to something we found when calculating the acceleration with the torque: higher gears let you go faster, but decrease the amount of acceleration. There is no getting around this. So now we have two relatively simple ways of finding the acceleration of a car at any given moment:

1. The torque at the wheels, found by multiplying the engine torque and gear ratio.
2. The power output of the engine and the velocity of the car.

So in the end, what is it that really does matter? To such a difficult question, I find it neccessary to give a cryptic answer: it depends on what you’re trying to do! In a perfect world, engines would have infinite amounts of torque and power, and the acceleration would be limited by the friction coefficient of the tires. Unfortunately this isn’t the case, so we must settle on a compromise between power and torque. With common engine technology, the camshaft profile and timing has the largest easily changed effect on where the engine’s peak torque is in the rpm band. Due to this limitation, engines usually focus on low end, midrange or high end torque. The low end stuff is great for getting moving, especially if you’re moving a lot of weight. Good midrange torque makes for a very drivable car in almost all circumstances. High end torque translates to the most horsepower, which is good if you want to go really fast all the time, though it usually comes with the cost of reduced acceleration. One way to avoid this compromise is to use variable valve timing, but this is out of the scope of this article.

For high speed racing, like F1, having as much power as possible is what wins races. This can be seen by the design philosophy of the engines: Astronomical rev limits to get the most amount of power out of an engine that can develop limited amounts of torque. It’s not every day that you see normally aspirated 2.4L V8’s putting out 700-800hp. They can do that thanks to the rpm that the design allows. Remember that hp = torque * rpm / 5252. We can solve for torque in this case to find that at the rev limit, the F1 engines are making around 200 ft-lbs of torque. This is still very impressive for the displacement, but not nearly as high as the power output. Conversely, engines with a very low rpm limit, like diesel engines, must generate massive amounts of torque to make any reasonable amount of power.

For rally racing, having as much acceleration as possible available to you at any moment is imperative. As such, we want an engine that has a very broad torque and power curve with good responsiveness. Gobs of torque down low, without sacrificing the top end is ideal for maximum performance in the varied conditions that rally cars encounter. As such, compromises are usually made to focus on midrange torque, which will still offer decent low end and top end power. This is the design path we will follow when we start doing engine modifications to our car.