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Old 16th December 2005, 19:08   #1
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Cool Physics behind car's movement

I thought a technical description of how the car moves (physics theory) will be good for the forum.
Some part of the article borrowed from internet. But I also added my comments as well.
Hope it will clear all confusions regarding Power Torque and Optimum Gearshift questions!


Relation between Power, Torque and RPM


In the automotive world, lots of things move in circles rather than in straight lines. Think of the wheels or engine. Distance is no longer meters, it is revolutions measured in radians. Speed is revolutions (or radians) over time instead of distance over time, for example, revolutions/minute (RPM) or radians/second. Mass is called inertia. We still need some kind of "push" to get something spinning. Instead of force, we have torque which is "twisting" force so to speak. Like force, torque must be applied to get something to spin faster or slower (acceleration).
This scenario is analogous with lever system. We know, for a lever F1*d1 = F2*d2. Where F1 >> F2 but d1 << d2. So by moving the lever a greater distance we can lift enough load though the work done in both cases are same. As I already said, in automotive world, the force is equivalent to torque and distance is equivalent to rotation. That means, by rotating a wheel more, we can generate higher torque on it (though power delivered to wheel remains the same in fact a bit less because of frictional loss)! Using gears, we just supply more torque to road wheels, so that the car can move! As engine revs faster and faster, torque rises (to a certain limit and then it falls). Using gearbox, the torque at engine's flywheel is multiplied at road wheels. When this torque produces enough force at the wheels, the car moves. Thus the main function of a gearbox is to act as a torque multiplier so that road wheels get enough power to pull the car.
Torque is measured by the amount of force applied tangentially at a given distance and that is force * distance (Nm = Newton meter).
Work in the rotational world is still basically force*distance. Torque is our force and distance is our revolutions in radians (1 revolution = 6.28 radians or roughly 2*pi). We use the same units such as Nm. The reason the units do not change is that the distance (radians) is a dimensionless quantity.

Power = Work / time
= Force * distance / time
= Torque (Nm) * revs (2*pi radian distance per second)
= Torque * revs/min * min/60s * (2 * pi)
= Torque * RPM * 0.1

or

Horsepower = torque * RPM * 1/5252 (in FPS unit)
1 ft-lb = 1.35 Nm and 1 HP = 0.746 kW

Usually max power occurs at a higher RPM than max torque in most car engines.
Now let us see what happens when you start car from rest.
A car is moved gradually when started. At this state, engine revs slowly – thus it can't produce enough power to road wheels to move the car. But, even at low rev, engine does develop some torque. Using gearbox (say 1st gear), this torque is multiplied several times (appx. 15-20 times in most cars). Now the torque produces sufficient power to the road wheels to enable the car to move. As engine revs higher, torque becomes less dominant and engine itself can generated enough power to make the car move. So for this reason, you usually shift to higher gears as speed rises. After 60 km/h you can use top gear in most cars.

Thus we note following points.

Engine's power becomes dominant in high rev and high speed. In fact, what will be the car's max speed depends on engine's power.

At low speed, it is torque, which moves the car.

For this reason, all car engines produce max torque at lower RPM and max power at higher
RPM (just examine any engine's power torque curve)

Torque is the deciding factor for a vehicle's traction – i.e. how much load it can pull. For this reason, truck engines are designed to produce very high torque at comparatively low rev. Also, diesel engines produce more torque than petrol engines (of same size). This also explains why truck engines are usually diesel engines.

It is possible for a car engine to pull huge load (increasing torque using several gears) as of a truck engine. However, to produce the required torque, the car engine has to rev at very high RPM, which will make the engine seize very soon and will use too much fuel (which is thus not economical)!
Usually an engine's idle speed is around 800 – 1000 RPM and a car's starting (just moving from rest) rev is around 1200 – 1500 RPM.

An engine's torque peak will be found when it finds its maximum volumetric efficiency. This is the point when the bores are most completely filled with mixture. If you can accomplish this at a low RPM (as most engines do) you can start applying your force sooner. You have more power, more twisting force on the axle.

When a car moves, it works against 3 kinds of resistance – resistance due to friction, resistance due to air drag (negligible at low speed, very much considerable at high speed) and resistance due to gradient.

How to increase torque in engine?


The physics behind engine power can generally be lumped into three areas, mechanical efficiency, volumetric efficiency and thermal efficiency.
Shaping the torque curve to fit your needs is quite simple with a computer program and the following logic: Mechanical efficiency mainly has to do with friction or parts of the engine that rob power. Volumetric efficiency can be thought of as how well the engine breathes. Thermal efficiency is the concept of heat and what happens to the heat.
Generally this is what you can expect improving the mechanical efficiency will increase the torque a little at the upper end RPM range. The peak of the torque curve tends to follows the peak volumetric efficiency. In other words, if the peak volumetric efficiency is at a lower or higher RPM then so is the torque peak. An increase in thermal efficiency tends to take the whole torque curve and move it higher on the torque scale.
In most engines, maximum developed torque is usually around 100 Nm/L.

Gear shift

You need to remember two things. You can shift gear for performance and for fuel economy.

If you want maximum acceleration, then you should shift gear in redline (maximum engine RPM). Theoretically, maximum acceleration is achieved when engine is producing maximum torque. Of course, that happens at lesser RPM than redline. However, when you shift up, engine rev decreases. So, if you shift up at maximum torque RPM, then after shifting up RPM decreases and thus torque decreases further in newer (higher) gear. But when you shift up at redline, engine RPM do decrease after shifting up, but that decreased RPM value is often near peak torque RPM value. So, you get good acceleration again in the newer (higher) gear.
However, you don't always shift up just for peak acceleration. For most normal driving, fuel economy is a major concern. Usually engine uses least fuel when revving around moderate RPM (mostly 2000 - 4000). So, you can shift as soon as possible provided sufficient power is available (either from torque multiplication through gearboxes or directly from engine flywheel) to road wheels to pull the car in higher gear in that speed. It means, when drivers say that you need to shift gear depending on judgment, they are quite right!


Car Resistance

When a car travels, it works against 3 kinds of resistances, viz. air, friction and gradient.
Total car resistance = Air resistance + Friction resistance + gradient resistance
We know, power = force * velocity
So, the power required to move a car in velocity V is
POWER reqd = (Cd*r*A*(V^2)/2 + u*m*g + m*g*sin(q))*V
where
Cd = coefficient of drag (usually 0.2 to 0.35)
r = air density (1.3 kg/m3)
A = frontal projected area of the car (~1.5 m2)
V = velocity of car (m/s)
u = coefficient of friction (~0.015-0.035 for rubber tyre on concrete road)
m = mass of car (kg)
g = acceleration due to gravity (9.8 m/s2)
q = gradient (or slope) of the road (radian) equals 0 on level ground
P = power required to move the car (W)

At low RPM, usually power is developed from torque multiplication (using gearbox). So, you start the car in lower gear. As speed rises, engine can gradually develop enough power to accelerate the car. So, you then shift to higher gears.

Now power available in the car is

Power (from torque) = Torque * RPM * 0.1 => calculate from torque curve
Power (directly at flywheel from RPM) = as obtained from engine power curve

Available power is the HIGHER of the above two values.
When, available power is more than required power the car accelerates!

Sample Power Torque curve



Ref:
http://www.off-road.com/hummer/tech/power.html
http://www.howstuffworks.com
http://www.auto-ware.com/combust_bytes/p_goal.htm

Last edited by sbasak : 16th December 2005 at 19:12.
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Old 9th January 2006, 17:55   #2
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Quote:
Originally Posted by sbasak
Relation between Power, Torque and RPM




Engine's power becomes dominant in high rev and high speed. In fact, what will be the car's max speed depends on engine's power.

At low speed, it is torque, which moves the car.

For this reason, all car engines produce max torque at lower RPM and max power at higher
RPM (just examine any engine's power torque curve)

Torque is the deciding factor for a vehicle's traction i.e. how much load it can pull. For this reason, truck engines are designed to produce very high torque at comparatively low rev. Also, diesel engines produce more torque than petrol engines (of same size). This also explains why truck engines are usually diesel engines.

It is possible for a car engine to pull huge load (increasing torque using several gears) as of a truck engine. However, to produce the required torque, the car engine has to rev at very high RPM, which will make the engine seize very soon and will use too much fuel (which is thus not economical)!
Usually an engine's idle speed is around 800 1000 RPM and a car's starting (just moving from rest) rev is around 1200 1500 RPM.

A very good job done.

But there is some confusion between power and torque. The power and torque are always inter-related. They can never be seperated out. If the engine is idling at say 1000 rpm, there is some torque and power, and when the car is moving in highest gear at 1000 rpm, then the torque and hence power produced is very high compared to idling conditions. So you can see that although rpm is same but torque and power have changed.

The torque/power curves given for any vehicle engine is not the one which you are likely to obtain on day to day basis but the maximum which engine can develop without any problems (like stalling etc).

As per your formula, you can see that power required is increasing with the speed and the resultant torque loading on the engine is also increasing. If plot them on graph for each gear ratio, in higher gear ratio (4th of 5th), a point will come where the torque required to increase the car speed will cut the curve of torque developed at the respective engine speed. The car won't accelerate beyond that point and the engine speed will automatically get limited to that rpm. But when the torque required curve for car does cut the torque available from engine at any point (lower gears), then car can continue to accelerate till the engine rpm limit is reached. Thus when you are cruising at say around 2000 rpm (assuming it is a diesel engine and max torque occurs at 2000 rpm), then it means that the actual torque developed by engine may be much less - say 40% of the max torque and you have enough margin to quickly accelerate.

Max torque produced by diesel engines is higher than petrol engines, but petrol engines have a flatter and hence better torque characteristics.

Pulling power is dependant on overhaul max bhp - if a 140 bhp petrol engine is used to replace a 90 bhp diesel engine on a truck and suitable gearing is used, the petrol engine will have higher hauling power than the diesel engine.

Also please note that it is always the torque and bhp is the calculated result, and not torque at low rpm and bhp at high rpm.

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Old 9th January 2006, 21:35   #3
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Quote:
Max torque produced by diesel engines is higher than petrol engines, but petrol engines have a flatter and hence better torque characteristics.
Modern diesel engines (eg. Mercedes, Honda etc.) usually produce higher torque than petrol engines and more importantly, then can hold this torque over a large RPM range (2000-3500).

Usually because of their inherent characteristics (high compression ratio etc.) diesel engines produce more torque than petrol engines. Torque is usually responsible for carrying load at low RPM (hence speed) that's why buses and trucks use diesel engines.
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Old 14th January 2006, 00:44   #4
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Quote:
Originally Posted by sbasak


Torque is usually responsible for carrying load at low RPM (hence speed) that's why buses and trucks use diesel engines.


I think there is some "ladki neeche khari hai" (misunderstanding).

What I mean is that torque is always repsonsible whether at low rpm of high rpm. You can measure torque (or to be precise, strain) and not the bhp directly. It is always calculated, whether manually or by measuring devices but is not measured.

We go by example below.

Let us say that you are pushing a package weighing around 10 kg at a constant speed. You will be applying a constant force to maintain a constant speed. If you want to accelerate to higher speed, again you will be increasing the force applied. Now if the weight of the package is increased to say 20 kg, then to push it at earlier speed of 10 kg package, you will now have to apply higher force. Also now if you have to increase the speed, you have to increase force. Now imagine a stronger person who can apply more force, starts the exercise initially with 10 kg package with both the speeds and the with 20 kg package and both the speeds, exactly the same way you have carried out these exercises. The force applied with remain same as you have applied altough he is stronger than you. You will find that in entire exercise we have always mentioned about force and not the power. Power will be calculated at all the events, but we have always been talking about force and not power. If we replace the force with torque in case of engines, the results are same. It is the torque everywhere, whether the rpm is low or high is immaterial. And bhp cannot exists without torque.

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Old 19th January 2006, 02:21   #5
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Default Torque-BHP with curves for Ikon1.3 and CRDi

http://www.team-bhp.com/forum/iipcache/19810.jpg

[img=http://img68.imageshack.us/img68/9112/diesel2wz.th.jpg]
http://img68.imageshack.us/my.php?image=diesel2wz.jpg

To understand the car movement better, Please see the images prepared by me. One is for diesel engine (Accent CRDi) and other one is for petrol engine (Ikon 1.3). To find out the actual torque characteristics, the torque produced are transferred to wheels. How? Well I have assumed that there is no loss of energy in transmission system and calculated the torque at wheels by multiplying the engine torque with transmission gear ratio from engine to wheels. The torque in 5th gear is in PINK, 4th gear is in YELLOW and 3rd gear is in BLUE. The torque cting on wheels due to resistance to movement of car is shown in BLACK.

RPMs for petrol engine 1000~5500
RPMs for diesel engine 1000~4000

The car will continue to accelerate as long as there is excess torque available at wheels, that is the engine torque line is above the torque line due to car resistance. We can see the PINK line (5th gear torque curve) for petrol engine cuts the BLACK line at around 140 KPH. That means the car maximum speed has reached. Similarly if we check the YELLOW line (4th gear torque curve), we can see that it cuts the BLACK line at around 150 KPH. This means that under the prevailing driving conditions, car can do around 150 KPH in 4th gear. If the car is goind uphill, or has more passengers and luggage or wind is against, the BLACK curve will move UP and it will cut the PINK and YELLOW curves earlier and hence the maximum speed will reduce. When the load is decreased, the BLACK curve will move down and hence, the maximum speed will increase.

When car is running at a steady speed, the torque produced by the engine is not as per the coloured lines but at per the BLACK line and power produced will be the TORQUE read from BLACK line times the RPM (converted to angular velocity)!!!. In this case the rpm will be the rpm of DRIVING WHEELS and not ENGINE.

Suppose you are moving at steady 40 km/hr and then you press the accelerator, the torque produced moves up vertically (in case floored, the torque produced by engine moves to PINK line - if you are 5th, or YELLOW line if you are 4th and if permitted by ECU to reach that line) and the car surges ahead. Depending upon the difference between BLACK line and the actual torque produced by engine, you will feel the surge, if the difference is quite high then you will feel yourself being pressed against the seat.

What happens if the maximum torque (the value remains same but rpm changes) produeced is closer to redline rpm than idling rpm (in NHC Vtec, it is closer to max rpm)? Then the torque curve gradient is less and it rises slowly and starts to dip at later speed. If we follow the petrol charateristics curve, then we can observe that there is not much change at 5th gear conditions (and hence 5th gear max speed won't change much-if max torque is very close redline, then 5th gear max speed will become less) but 4th gear gear line (YELLOW) will continue to run almost straight and hence the max speed reached will go up to almost 160 km/hr (although there is no change in BHP and torque values).

What happens when the torque is close to idling rpm (in NHC iDSi, it is closer to idling rpm)? The YELLOW curve will rise to max earlier. Hence there will be more torque at wheels available and thus it will have more pulling power. It improves driveablility at lower speed. (That's how NHC has been able to maintain good acceleration values in spite of having so low power). Aslo imagine that the car is overloaded with lots of luggage and people (which is common in India) and thus BLACK line moves almost close to PINK line or may touch it. This means you have to shift down to keep your vehicle moving smoothly
without the fear of engine stalling. But if your maximum value occurs close to idling rpm (say around 40 kph and value will be 325 instead of 250 as shown in graph by PINK line), then you don't have to shift down. This is described as "diesels have more lugging power than petrol engines". But the torque curve will start dipping early and hence will cut the BLACK line early and therefore the max speed will also become less.

I will leave it other members to analyse and compare petrol curves with diesel curves.

In all this discussion, we have always come across torque only and no where we have seen BHP crop up. If everything is done be torque, then why BHP is used? Well, to compare the diesel and petrol engines, we have transferred it to tyres (boths cars
have same tyres and offers similar resistances - please note that even if they are different, corrections can be applied) and hence have been able to keep the rpm out of discussion. What if we have to compare a truck engine to a car engine or fit the same engine on truck and car? Or the same engine has to be fitted in boat and therefore there is no wheels in comparison. Then BHP comes into play. For example a let us assume one diesel engine is developing 80 ps at 4000 rpm and another petrol engine 100 ps at 6000 rpm. How do we compare? Diesel engine with 80 ps will have a torque equivalent of around 80/4 = 20 while petrol will have 100/6 = 16.7. So petrol engines looks like to be a weaker as it has less torque at its max power. But now we trnsfer the petrol torque to diesel equivalent to 4000 rpm then it will 16.7*6/4 = 25 and you can see that the weaker
petrol is actually more powerful than diesel one and has more pulling power. Thus ultimately the power matters in the comparison. And this is described by many people as "while torque works in lower rpm, bhp works in higher rpm". But torque is still there, isn't it? Because without torque bhp simply cannot exist. That is TORQUE (ZERO) times RPM will always be ZERO.

I hope the above discussion will not be cause of boredom.


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Old 26th January 2006, 23:41   #6
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Default The importance of Gear No. 1

If we look at the torque map for different gears at lowest speed, we will notice that it appears that therei is sufficient net torque available to move the car from idling speed. And when we try in second or sometimes third gear to drive away, the engine is able to pull the car. It stalls in higher gears (high powered cars would be able to pull away in higher gears also). If you have tried to push a car in neutral, you would have noticed that you can easily move the car from its place but unable to move it fast. That means to move the car from standstill, you don't require huge torque.


If the car is able to pull away neatly in 2nd gear, then why is the first gear provided. If we look at the gear ratios, we will observe that the lowest speed is in first gear (approx - 5~7 kmph) with highest torque at wheels. As we move up the lowest speed increases say 12~15 kmph in 2nd, ~20 kmph in 3rd, 27~30 in 4th and 35~40 in 5th.


Now we can observe two things:
1. That when very low speed is required e.g. during parking etc for better control of vehicle, the first gear is the ideal.
2. Suppose, it is possible to start moving in 5th gear without stalling the engine. Then the car will be accelerating from standstill to ~ 40 kmph in very short time, say 0.5 sec. Now imagine that a bulk of 1~2 tons to be moved in such a short time. This is something like the standstill car being hit by a truck moving at 40 kmph from behind. Now you can imgine the load or stresses on the transmission parts, body, clutch, tyres etc and the engine itself. And the condition of the passengers. Therefore to reduce the stresses, first gear is used to move from standstill. Higher the gear used (without stalling), more the load or if clutch is used to reduce the accelaration, then more wear and tear of clutch. This is there because of inherent property of the engines - they can not operate below a certain minimum rpm.


So the question is if we can develop some torque at ZERO rpm, do we require the high gear ratio as in first. The answer is no. Let us take an example of electric motors. If we supply a small voltage, there will be torque (although motor won't be producing any power as rpm is nil). If this torque is more than the resistance offered by the car, the car will move smoothly from standstill. If this torque is very high, the car will shoot like a rocket. Now once the car starts moving, the motor will generate some back emf (voltage) to oppose the voltage being supplied. If we increase the supplied voltage to keep the difference between the supplied voltage and back emf constant, then we can have a constant torque on the wheels. We can continue to increase the voltage till it reaches the max safe value for the motor. We can note here that there is no changing of gear involved (FYI - it is possible to have electrical gear ratios). Therefore the electrical motors can operate from ZERO rpm to max rpm without any gears (and also without clutch) and are able to utilse the max power unlike the engines which due to mech gears are unable to do so.
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Old 27th January 2006, 15:12   #7
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Therefore the electrical motors can operate from ZERO rpm to max rpm without any gears
That's why railway electric locomotives don't have gears! Also, steam locos don't use gear either. They can generate enough pressure to employ tractive effort depending on load (that's a long story anyway). In railways, only the diesel-hydraulic (rarely used now) locos use gears because they use exactly same method as of automobiles. Standard diesel locos (known as diesel-electric locos) also generate electricity and fed to traction motors in wheels. There are several complex factors why this diesel-to-electricity approach is used but one major reason is that under such huge load (a train weighs over 1500 ton) a clutch will always slip!

The gigantic dump trucks is probably the only road vehicle where a generator is used to produce electricity and which is fed to traction motors on its wheels.
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Old 6th February 2006, 17:33   #8
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Sorry - posted in wrong place (copy paste goof up).Moderators: Please delete this post.

Last edited by sbasak : 6th February 2006 at 17:36.
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Old 11th February 2006, 16:21   #9
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Awesome thread! Since it says physics thought I'd add ".5mV^2"(v = velocity and m= mass since alot of people eem toget carried away with the bhp/tonne figures.

From the equation, if you need topull four times the load you only need twice as much power, however if you want to go 4 times faster you need 16 times as much power.
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Old 14th February 2006, 01:01   #10
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REALLY amazing info..... Have to alll u guys, esp. Sbask and Jat....are u guys students or school or in college ?? thakns a lot for all the info guys !!!!!
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Old 16th March 2006, 21:19   #11
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small addendum, if readers wouldn't mind... sometimes perhaps small is clear.

let's consider a petrol & diesel engine of same capacities, in two cars of SAME WEIGHT.
a rule of thumb for petrol engines - more power, less torque.

torque is pulling power. a diesel car will pull heavy loads unlike the petrol car since it has lots of torque. the petrol car zips faster - because the engine produces more bhp than the other's. don't confuse acceleration with torque. torque refers only to the ability of a car to haul/pull. even little trucks with no more bhp than an OHC will haul tonnes over a gradient (of course, at crawling speeds) - a feat the OHC may not be able to achieve. TORQUE IS NOT ACCELERATION. IT IS HAULING ABILITY.
torque is different at different engine speeds. the MAXIMUM PRODUCT of engine speed and corresponding torque is the MAXIMUM POWER of the engine. so they aren't two independent entities at all - torque being a part of power.

acceleration is a result of certain torque being produced at certain rpm, and so depends on the torque and power curves at different engine speeds. it does not depend on torque alone. it depends on THE PRODUCT of torque and velocity - which is the same as bhp.

THIS HAS TURNED OUT TO BE LONGER THAN INTENDED. AND PERHAPS AS A CONSEQUENCE, NOT AS CLEAR AS WAS INTENDED...

Last edited by skandyhere : 16th March 2006 at 21:21.
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Old 30th April 2006, 19:19   #12
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Hi
The info is great. For a layman like me i wpould like to ask a simple question which i would appreciate if answered with a very simple example

Q> Gypsy produces 45bhp at 5500rpm and a torque of 7.5kg as compared to gypsy king which produces 80bhp at 5500rpm anda orque of 10.5kgms. Gypsy is 1000cc while the king is 1300cc

1>Now taking this example tell me if i have to traveses a plain road of 200km what things will affect pickup to top speed.

2> If say both cars are on a incline how will the factors affect the pick up with respect to achieving top gear

3> since both are 4wheel drive what sort of mechanics take place when thses cars are put in 4 wheel normal mode or Loading mode(4L)

4> Is it possible to increase the bhp ???

I hope i have not asked much
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Old 2nd May 2006, 19:22   #13
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Quote:
Originally Posted by skandyhere

petrol engines - more power, less torque.

...
I disagree

To compare two engines, we have to compare equivalent force available at the point of contact between the wheels and road. That means more power > more torque.

This rule has been made by God or nature and not human being.
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Old 2nd May 2006, 19:25   #14
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Quote:
Originally Posted by skandyhere
.... don't confuse acceleration with torque. torque refers only to the ability of a car to haul/pull. even ...
Torque = J x alpha

J = Moment of inertia
alpha = acceleration

So torque has to be accelaration.

And again this rule is made by God.
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Old 2nd May 2006, 19:26   #15
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Quote:
Originally Posted by skandyhere
a feat the OHC may not be able to achieve. TORQUE IS NOT ACCELERATION. IT IS HAULING ABILITY.
...
OHC engine will always be able to achieve more hauling power if fitted to the truck compared to a lower power diesel engine.

This rule has been made by HONDA guys.
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