You have to eat broccoli first for this to work. Its like adding nitro methane to a car.
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I read some of posts above, that says torque is force. This isn't correct. Without going into tractors, let me write relations between hp (power), torque and force.
Lets start with their units (using SI units):
Force: N (Newton) ~ kg x m / sec^2 (that's, mass x acceleration.)
Torque: Force x m ~ Nxm (that is, Work done at a meter by a force. Torque is the name of moment at angular motion.) So, moment or torque (angular motion like crankshaft or pto) has a unit of work, energy.
Power: Watt or HP ~ Work / sec. That's, work done per unit of time. So, we can say that HPower is Torque per second.
So, from equation: HP = TORQUE per TIME
HP1 = TORQUE1 per TIME1
HP2 = TORQUE2 per TIME2
IF torque1 and torque2 are same for 35 hp and 37 hp,
tractor1: 37 = torque / time1
tractor2: 35 = torque / time2
Divide these two equations by each others; you have
37 / 35 = time2/time1
Which means time2 is bigger than time1, which means work (energy, torque) can be done at a shorter time period by tractor1 which has 37 hp. Peaks can be same, but, areas under force-torque-energy curves are different. 2 takes more time, 1 takes less time. So, same torque more hp can be useful for more instant load (more shock) applications while less hp with same torque can be useful for slower load applications. However, I don't think these 35 and 37 horsepowers (small difference) for same peak torques are for application classifications. It is probably due to production tolerances. One of them is about 2% safer in claim as they gave smaller, 35, hp. Or, 37 hp one has really higher production tolerance.
PS: looking back to original post which says 31 and 37 hp and by same company JD, then, these two tractors are for application classifications. With the explanation of hp and torque above, 37 hp will be more useful for instant load applications such as cuttings while 31 hp with same torque will be enough (a little cheaper as well) for slower applications such as raking.
To see if it adds anything, I did a search of "Power mechanical omega Tau" on Google, and this page comes up:
Torque - Wikipedia, the free encyclopedia
And the units sections says that the SI literature suggests that Tau can be expressed in either Newton*meters or joules/radian.
So Pmech is (radians/ second) * (joules/radian) and the radian term cancels leaving joules/second which is a term of power.
So I think nomad is quite correct. Sometimes I get confused about it and although my math always works, I would have called tau torque rather than moment because that is what the electrical professors taught. But I do now remember thanks to Nomad that in my mechanical courses, they called it moment.
Bota, yes, people in general, even schooled/engineering ones are sometimes confused about the torque.
This is usually due to forgetting scalar and vectorial quantities.
Force and moment / torque are vectorial quantites (scalar magnitude is not enough for exact identification of quantities, directions too should be given together with scalar quantity for exact identification.)
Work, energy, mass, temperature, pressure, etc are scalar quantities, point quantities, direction independents.
Power is always energy (work too is energy) per unit of time.
Difference between torque and moment is torque is for rotational motions in using equation forms actually. Moment is usually calculated in cartesian coordinates; x-y-z as motion is cartesian, linear. Hence, usually, moment equation is given in form of "Force x Distance" which is equivalent to Work (energy), except that moment also has a direction while work doesn't.. In case of torque, we engineers usually use rotational speeds, rpm (or angular speed in radyan per time) in energy or power calculations. That's why we see equation form of energy or power as "torque x rpm x some constant." So, torque too has a direction just like moment. But, their scalar magnitudes of moment and torque is an Energy quantity like N.m (lbxft/sec^2). That's why I say torque or moment are in the same class with energy or work with a small difference, direction too needs to be given to identify moment / torque exactly, which is usually forgotten in daily life.
As it is seen on Wiki, multiplications of vectorial quantities are different than multiplications of scalar quantities which we generally use in daily life. In multiplication of vectorial quantities, called cross product, directions too are multiplied (by known right hand thumb rule.) Tangential forces on the pto shaft rotate the pto shaft with a radius of r.
So, torque or moment of pto is "Tangential force x radius" which both are vectorial quantities, output, torque too is a vectorial quantity.
So, when torque of a pto is identified, it is a pair, a scalar and a direction, eg, "100 N.m, perpendicular to shaft axis." Confusion is usually due to omitting / forgetting that direction.
Ps: Sorry, it was like a school course, but, I saw Wiki page for people with engineering language. I tried to simplify things here for people foreigner to engineering language.
Ok, I gave a relation (not equation actually, but, equivalency) above in my previous post; as HP1=Torque1 per Time1 etc. Following this, generating further, HP2 = Torque2 per Time2, etc - we can understand and compare torques and hps of different tractors.
My brain hurts now, though I do understand at a remedial (not an engineer) level.
No need to be sorry about a thing. What you wrote was complete, and upon looking into it from my memories on the matter, I formed a search and found something I didn't know and found interesting, so I added it. I didn't know that tau could be rightly expressed in joules/radian.
As you know, radian is a unit-less, dimension-less quantity actually. So, you see, tau (torque) is expressed in terms of joules actually, that is, work or energy quantity. But, its magnitude only, i.e. its scalar value of a vectorial quantity tau or torque which also needs its pair, direction to make its exact identification which people usually disregard in their daily lifes especially for simple rotational items like pto. When engine is designed, all directions of all turning parts are taken into account of large calculations of torques etc which are later used to calculate powers.
Anyway, returning back to topic, period of time needs to be considered in understanding power as it is always a quantity, a scalar quantity, this way or that way,devided by a period of time which is not included in force or energy or work or moment or torque which all are instant / point quantities.
PS: Brain55, not to make your brain hurt more, thank to Newton, classical mechanics in which time is steadily changing linear value. If we were using Einstein mechanics, time too would have been another dependent factor which should have been calculated seperately.
(just to clarify and simplify further, relating to topic, with a language common can understand.)
Power = Torque x RPM x Some constant
(this "some constant" can change depending on what units (si, lb-ft, watt, hp, sec, minute, hour, etc you are using. So, this constant isn't so important in understanding physical meanings of quantities.)
RPM = Revolution per Minute, that's, elapsed a unitless quantity per time. Note: 2*pi radian, 360 degree is one revolution. So, since revolution is a dimensionless quantity RPM can also be written as "1/min" sometimes. As seen here, this rotational speed, rpm or 1/min is not a speed like ft / min, but, 1/min.)
So, when calculating HP by using Torque, actually, you are multiplying by 1/minute or in another words, you are dividing Torque by minute, time indirectly. Just like dividing Energy by time.
So, we can obtain this form HP ~ Torque / Time. (not equation =, but, I used ~ to understand their relationship. When we multiply by some constant, we obtain equation, =..
So, for our need here, for understanding HP and Torque relation of, knowing this relation will be enough for comparisons and no need to know "some constant" unless you need to calculate "exact values." So, say, for a tractor, we also need to know TIME elapsed in an application. Elapsed time can change according to application. As an exaggerated example, in a shock application like sudden cutting and in slow application like slow raking hay, time periods elapsed will be different, hence, either torque or hpowers will differ. So, either HP or Torque matters depending on your application.You know, in a car, if your need is speed, high speed, go for higher HP less torque. Tractor driving or attachment application won't be different. If peak torques of two different HPs are same, chose bigger HP for quick/fast applications like cutting as extra amount of HP will be used for speed of tractor. (after long posts, I guess, I am clear enough.:)