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Reference: A Phyiscs Lesson

Discussion in 'Engine Tech / Drivetrain DIY How-To's' started by Eran, Jan 29, 2006.



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  1. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    A Phyiscs Lesson <ALL SHOULD READ>

    Mass
    Mass is defined as the measure of how much matter an object or body contains -- the total number of subatomic particles (electrons, protons and neutrons) in the object. If you multiply your mass by the pull of Earth's gravity, you get your weight. So if your body weight is fluctuating, because of eating or exercising, it is actually the number of atoms that is changing.

    It is important to understand that mass is independent of your position in space. Your body's mass on the moon is the same as its mass on Earth, because the number of atoms is the same. The Earth's gravitational pull, on the other hand, decreases as you move farther away from the Earth. Therefore, you can lose weight by changing your elevation, but your mass remains the same. You can also lose weight by living on the moon, but again, your mass is the same.

    Mass is important for calculating how quickly things accelerate when we apply a force to them. What determines how fast a car can accelerate? You probably know that your car accelerates slower if it has five adults in it than if it has just one. We'll explore this relationship between mass, force and acceleration in a little more detail after we talk about force.
     
  2. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Force
    Force causes acceleration. If you apply a force to a toy car (for example, by pushing on it with your hand), it will start to move. This may sound simple, but it is a very important fact. The movement of the car is governed by Isaac Newton's Second Law, which forms the foundation for classical mechanics. Newton's Second Law states that the acceleration (a) of an object is directly proportional to the force (F) applied, and inversely proportional to the object's mass (m). That is, the more force you apply to an object, the greater the rate of acceleration; and the more mass the object has, the lower the rate of acceleration.

    When the car begins to accelerate, some new forces come into play. The rear wheels exert a force against the ground in a horizontal direction; this makes the car start to accelerate. When the car is moving slowly, almost all of the force goes into accelerating the car. The car resists this acceleration with a force that is equal to its mass multiplied by its acceleration. You can see in Figure 1 how the force arrow starts out large because the car accelerates rapidly at first. As it starts to move, the air exerts a force against the car, which grows larger as the car gains speed. This aerodynamic drag force acts in the opposite direction of the force of the tires, which is propelling the car, so it subtracts from that force, leaving less force available for acceleration.

    Eventually, the car will reach its top speed, the point at which it cannot accelerate any more. At this point, the driving force is equal to the aerodynamic drag, and no force is left over to accelerate the car.
     
  3. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Torque
    Torque is a force that tends to rotate or turn things. You generate a torque any time you apply a force using a wrench. Tightening the lug nuts on your wheels is a good example. When you use a wrench, you apply a force to the handle. This force creates a torque on the lug nut, which tends to turn the lug nut.

    English units of torque are pound-inches or pound-feet; the SI unit is the Newton-meter. Notice that the torque units contain a distance and a force. To calculate the torque, you just multiply the force by the distance from the center. In the case of the lug nuts, if the wrench is a foot long, and you put 200 pounds of force on it, you are generating 200 pound-feet of torque. If you use a 2-foot wrench, you only need to put 100 pounds of force on it to generate the same torque.

    A car engine creates torque and uses it to spin the crankshaft. This torque is created exactly the same way: A force is applied at a distance. The combustion of gas in the cylinder creates pressure against the piston. That pressure creates a force on the piston, which pushes it down. The force is transmitted from the piston to the connecting rod, and from the connecting rod into the crankshaft. In Figure 2, notice that the point where the connecting rod attaches to the crank shaft is some distance from the center of the shaft. The horizontal distance changes as the crankshaft spins, so the torque also changes, since torque equals force multiplied by distance.

    You might be wondering why only the horizontal distance is important in determining the torque in this engine. You can see in Figure 2 that when the piston is at the top of its stroke, the connecting rod points straight down at the center of the crankshaft. No torque is generated in this position, because only the force that acts on the lever in a direction perpendicular to the lever generates a torque.

    If you have ever tried to loosen really tight lug nuts on your car, you know a good way to make a lot of torque is to position the wrench so that it is horizontal, and then stand on the end of the wrench -- this way you are applying all of your weight at a distance equal to the length of the wrench. If you were to position the wrench with the handle pointing straight up, and then stand on the top of the handle (assuming you could keep your balance), you would have no chance of loosening the lug nut. You might as well stand directly on the lug.
     
  4. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Work and Power
    Work is simply the application of a force over a distance, with one catch -- the distance only counts if it is in the direction of the force you apply. Lifting a weight from the ground and putting it on a shelf is a good example of work. The force is equal to the weight of the object, and the distance is equal to the height of the shelf. If the weight were in another room, and you had to pick it up and walk across the room before you put it on the shelf, you didn't do any more work than if the weight were sitting on the ground directly beneath the shelf. It may have felt like you did more work, but while you were walking with the weight you moved horizontally, while the force from the weight was vertical.

    Your car also does work. When it is moving, it has to apply a force to counter the forces of friction and aerodynamic drag. If it drives up a hill, it does the same kind of work that you do when lifting a weight. When it drives back down the hill, however, it gets back the work it did. The hill helps the car drive down.

    Work is energy that has been used. When you do work, you use energy. But sometimes the energy you use can be recovered. When the car drives up the hill, the work it does to get to the top helps it get back down. Work and energy are closely related. The units of work are the same as the units of energy, which we will discuss.

    Power is a measure of how quickly work can be done. Using a lever, you may be able to generate 200 ft-lb of torque. But could you spin that lever 3,000 times per minute? That is exactly what your car engine does.

    The SI unit for power is the watt. A watt breaks down into other units that we have already talked about. One watt is equal to 1 Newton-meter per second (Nm/s). You can multiply the amount of torque in Newton-meters by the rotational speed in order to find the power in watts. Another way to look at power is as a unit of speed (m/s) combined with a unit of force (N). If you were pushing on something with a force of 1 N, and it moved at a speed of 1 m/s, your power output would be 1 watt.
     
  5. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Horsepower
    The term horsepower was invented by the engineer James Watt. Watt lived from 1736 to 1819 and is most famous for his work on improving the performance of steam engines. We are also reminded of him every day when we talk about 60-watt light bulbs.

    The story goes that Watt was working with ponies lifting coal at a coal mine, and he wanted a way to talk about the power available from one of these animals. He found that, on average, a mine pony could do 22,000 foot-pounds of work in a minute. He then increased that number by 50 percent and pegged the measurement of horsepower at 33,000 foot-pounds of work in one minute. It is that arbitrary unit of measure that has made its way down through the centuries and now appears on your car, your lawn mower, your chain saw and even in some cases your vacuum cleaner.

    What horsepower means is this: In Watt's judgement, one horse can do 33,000 foot-pounds of work every minute. So, imagine a horse raising coal out of a coal mine as shown above. A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. You can make up whatever combination of feet and pounds you like. As long as the product is 33,000 foot-pounds in one minute, you have a horsepower.

    [​IMG]

    You can probably imagine that you would not want to load 33,000 pounds of coal in the bucket and ask the horse to move it 1 foot in a minute because the horse couldn't budge that big a load. You can probably also imagine that you would not want to put 1 pound of coal in the bucket and ask the horse to run 33,000 feet in one minute, since that translates into 375 miles per hour and horses can't run that fast. However, if you have read How a Block and Tackle Works, you know that with a block and tackle you can easily trade perceived weight for distance using an arrangement of pulleys. So you could create a block and tackle system that puts a comfortable amount of weight on the horse at a comfortable speed no matter how much weight is actually in the bucket.

    Horsepower can be converted into other units as well. For example:

    * 1 horsepower is equivalent to 746 watts. So if you took a 1-horsepower horse and put it on a treadmill,
    it could operate a generator producing a continuous 746 watts.

    * 1 horsepower (over the course of an hour) is equivalent to 2,545 BTU (British thermal units). If you took
    that 746 watts and ran it through an electric heater for an hour, it would produce 2,545 BTU (where a
    BTU is the amount of energy needed to raise the temperature of 1 pound of water 1 degree

    * One BTU is equal to 1,055 joules, or 252 gram-calories or 0.252 food Calories. Presumably, a horse
    producing 1 horsepower would burn 641 Calories in one hour if it were 100-percent efficient.

    Converting Engine Torque to Horsepower
    Have you ever looked at the specs of an engine in a magazine and seen something like "this engine makes 300 pound-feet of torque at 4,000 RPM," and wondered how much power that was? How much horsepower are we talking about here? You can calculate how many foot-pounds of horsepower this engine produces using a common equation:

    (Torque x Engine speed) / 5,252 = Horsepower

    The engine that makes 300 pound-feet of torque at 4,000 RPM produces [(300 x 4,000) / 5,252] 228 horsepower at 4,000 RPM. But where does the number 5,252 come from?

    To get from pound-feet of torque to horsepower, you need to go through a few conversions. The number 5,252 is the result of lumping several different conversion factors together into one number.

    First, 1 horsepower is defined as 550 foot-pounds per second (read How Horsepower Works to find out how they got that number). The units of torque are pound-feet. So to get from torque to horsepower, you need the "per second" term. You get that by multiplying the torque by the engine speed.

    But engine speed is normally referred to in revolutions per minute (RPM). Since we want a "per second," we need to convert RPMs to "something per second." The seconds are easy -- we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you're left with a dimensionless measure.

    You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 x pi x radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the "per second" we need to calculate horsepower.

    Let's put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252.

    So if you multiply torque (in pound-feet) by engine speed (in RPM) and divide the product by 5,252, RPM is converted to "radians per second" and you can get from torque to horsepower -- from "pound-feet" to "foot-pounds per second."

    Measuring Horsepower
    If you want to know the horsepower of an engine, you hook the engine up to a dynamometer. A dynamometer places a load on the engine and measures the amount of power that the engine can produce against the load.

    You can get an idea of how a dynamometer works in the following way: Imagine that you turn on a car engine, put it in neutral and floor it. The engine would run so fast it would explode. That's no good, so on a dynamometer you apply a load to the floored engine and measure the load the engine can handle at different engine speeds. You might hook an engine to a dynamometer, floor it and use the dynamometer to apply enough of a load to the engine to keep it at, say, 7,000 rpm. You record how much load the engine can handle. Then you apply additional load to knock the engine speed down to 6,500 rpm and record the load there. Then you apply additional load to get it down to 6,000 rpm, and so on. You can do the same thing starting down at 500 or 1,000 rpm and working your way up. What dynamometers actually measure is torque (in pound-feet), and to convert torque to horsepower you simply multiply torque by rpm/5,252.
     
  6. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Graphing Horsepower
    If you plot the horsepower versus the rpm values for the engine, what you end up with is a horsepower curve for the engine. A typical horsepower curve for a high-performance engine might look like this (this happens to be the curve for the 300-horsepower engine in the Mitsubishi 3000 twin-turbo):

    [​IMG]

    What a graph like this points out is that any engine has a peak horsepower -- an rpm value at which the power available from the engine is at its maximum. An engine also has a peak torque at a specific rpm. You will often see this expressed in a brochure or a review in a magazine as "320 HP @ 6500 rpm, 290 lb-ft torque @ 5000 rpm" (the figures for the 1999 Shelby Series 1). When people say an engine has "lots of low-end torque," what they mean is that the peak torque occurs at a fairly low rpm value, like 2,000 or 3,000 rpm.

    Another thing you can see from a car's horsepower curve is the place where the engine has maximum power. When you are trying to accelerate quickly, you want to try to keep the engine close to its maximum horsepower point on the curve. That is why you often downshift to accelerate -- by downshifting, you increase engine rpm, which typically moves you closer to the peak horsepower point on the curve. If you want to "launch" your car from a traffic light, you would typically rev the engine to get the engine right at its peak horsepower rpm and then release the clutch to dump maximum power to the tires.

    A car is considered to be "high performance" if it has a lot of power relative to the weight of the car. This makes sense -- the more weight you have, the more power it takes to accelerate it. For a given amount of power you want to minimize the weight in order to maximize the acceleration.

    The following table shows you the horsepower and weight for several high-performance cars (and one low-performance car for comparison). In the chart you can see the peak horsepower, the weight of the car, the power-to-weight ratio (horsepower divided by the weight), the number of seconds the car takes to accelerate from zero to 60 mph, and the price.

    Code:
    [B]Car			BHP	Weight	Power:Weight	0-60 mph	Price[/B]
    
    Dodge Viper		450	3,320	0.136		4.1		$66,000
    
    Ferrari 355 F1		375	2,975	0.126		4.6		$134,000
    
    Shelby Series 1		320	2,650	0.121		4.4		$108,000
    
    Lotus Esprit V8		350	3,045	0.115		4.4		$83,000
    
    Chevrolet Corvette	345	3,245	0.106		4.8		$42,000
    
    Porsche Carrera		300	2,900	0.103		5.0		$70,000
    
    Mitsubishi 3000GT TT	320	3,740	0.086		5.8		$45,000
    
    Ford Escort		110	2,470	0.045		10.9		$12,000
    You can see a very definite correlation between the power-to-weight ratio and the 0-to-60 time -- in most cases, a higher ratio indicates a quicker car. Interestingly, there is less of a correlation between speed and price. The Viper actually looks like a pretty good value on this particular table!

    If you want a fast car, you want a good power-to-weight ratio. You want lots of power and minimal weight. So the first place to start is by cleaning out your trunk.
     
  7. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    *FINAL NOTES*

    I know I made a typo in the title. Pleas do not mention this :rolf:

    All this information is courtesy of HowThingsWork.com
     
  8. Handlebars

    Handlebars None Taken. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    this is the engine tech archive, not the lounge. any posts made are to be on point with the thread.
     
  9. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Ba-dump da dump. Everyone should read this shizzle.
     
  10. ShinsenTuner

    ShinsenTuner CC's Youngest OG Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    oh s**t son, i learned this last year haha
     
  11. J32a2OwnsU

    J32a2OwnsU Resident Old Man Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Sweet basic HS physics!!!!!

    Good info on the bottom part.
     
  12. Eran

    Eran It's on ass-backwards. Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    The sad part is .... some people don't know this stuff ... or don't understand how it applies to a car :???:
     
  13. J32a2OwnsU

    J32a2OwnsU Resident Old Man Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Thats true man.... sad... :(
     
  14. vandynamics

    vandynamics New Member Registered VIP 5+ Year Member 10+ Year Member

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    well written.
     
  15. 3DScott

    3DScott New Member Registered VIP 5+ Year Member

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    well i dont know some of this. Nice write up. >` Printing now!
     
  16. NOFX

    NOFX I'm NOT eran! Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Reference: A Spelling Lesson

    :P ;)
     
  17. JL

    JL Doodoo Brown Member Registered VIP 5+ Year Member 10+ Year Member

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    I've actually read this before on the same site a couple years ago. Good stuff.
     
  18. D16Y8Noob

    D16Y8Noob Respected

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    You should add Watts and kpm conversion to the end of HP section.

    Topics to consider for this thread: Viscosity; Vacuum and pressure; Ohms and kirchoff's Laws; resistance, inductance, capacitance, reactance and impedance; thermodynamics; frequency and resonance. Maybe some metallurgy so they can understand why there are several types of metal housings, nuts and bolts used in engineering.
    The list goes on, but one step at a time.
     
  19. XpL0d3r

    XpL0d3r What Civic? Staff Member Registered VIP Registered OG 5+ Year Member 10+ Year Member

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    Ah the classic 11 year old thread bump! :lol: :lock:
     
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