Work - Work is a measurement of a force acting through a distance. Example: lb-ft "pound-feet" or ft-lb "foot-pounds" (lb = force, ft = distance).
Power - Power is the measurement of the rate in which work is performed and therefore how much energy is consumed during a process. The units are therefore force through a distance per a unit of time. Power measures how much work is being done over a given time interval. Example: lb-ft/sec (lb = force, ft = distance, sec = time).
Horsepower - Horsepower is a simply a unit of power. It is defined under the assumption that a horse can move 33,000 lbs 1 foot per minute (1 horsepower = 33,000 lb-ft/min). Since there are 60 seconds per minute, horsepower can be reduced to 550 lb-ft/sec.
Torque - Torque is the measure of an objects tendency to rotate about a point. It is a measure of work, and in terms of engine output can be simply described as the net twisting force. Torque, which is measured about a fixed axis, is not a time dependent variable.
Horsepower vs Torque
Horsepower and torque are closely related concepts, yet it is relatively common for people to focus on the differences between the two. An advantageous method of approach is to understand the relationship between horsepower and torque.
Torque = (Horsepower x 5,252) / RPM
Horsepower = (Torque x RPM) / 5,252
A dynamometer actually measures torque and calculates horsepower using the formula above. Don't get confused by the 5,252, it is a mathematical constant derived from the fact that a 1 foot circle has a circumference of 6.2832 feet. Dividing 33,000 by 6.2832 gives you 5,252, which simplifies the equation and resolves the units. This constant is the reason that horsepower and torque graphs always cross paths at 5,252 rpm.
For the sake of practicality, the application dictates whether torque or horsepower is intuitively more significant and/or purposeful to an individual.
Minimum input for a given output - take a 10,000 Watt engine driven generator. The unit of Watts, most commonly used to describe electrical power output, is a unit of power nonetheless and can be converted to horsepower. Since 10,000 Watts is equal to 13.5 horsepower, the generator will require at minimal a 13.5 hp engine to run the generator at maximum capacity (ignoring pumping and frictional losses). Why? The first law of thermodynamics; energy in is energy out. Therefore, you cannot have an output that is greater than the input. The takeaway from this example is that torque itself is intuitively irrelevant in meeting the needs of our fictitious generator if a minimum power is not produced. If you wanted to know the minimum input for an application and were given engine torque at a governed speed, you would have to calculate the horsepower at that engine speed in order to declare whether or not you would be able to obtain your desired output power.
On the contrary, torque can be described as the tendency of an object to overcome an applied load. Take a winch, for example, attempting to pull a 10,000 lb pallet across a concrete floor. The torque (and corresponding force) required to pull the object is equal to the frictional force between the pallet and concrete slab. If we apply a torque to the winch cable drum below this minimum value, nothing happens. When we apply a torque equal to the minimum required value, the pallet begins to move towards the winch. In this example, horsepower is intuitively meaningless to the situation - we're really only concerned with producing enough torque to keep the pallet moving.
This brings up an important distinction between horsepower and torque. A torque can be applied at a point with zero rotational movement. Consider a rusty bolt that just won't budge. You place a long wrench on the bolt, then proceed to apply the enter weight of your body at the end of the wrench, but the bolt still ceases to rotate. There is a torque applied to the bolt at this point of time equal to the your weight x the length of the wrench. However, without rotational movement, there is no power.
In the application of automotive engines, torque is closely related to acceleration. In Newtonian physics, the acceleration of an object is equal to the net force acting on the object divided by the objects mass (Acceleration = Net Force/Mass). Since torque is simply a force applied through some distance, we can easily convert torque into a driving or propulsive force and then calculate acceleration.
PF = propulsive force (the driving force of the vehicle)
NF = the net force acting on the vehicle
RF = the net resistive force acting on the vehicle (this includes friction between the tires and the road and wind resistance).
A = rate of acceleration
FDR = final drive ratio
DWT = drive wheel torque (torque applied to the drive tires)
1) FDR = transmission gear ratio x differential ratio
2) DWT = engine torque x FDR
Assuming that, for the sake of simplicity, we ignore all parasitic losses in the drivetrain
3) PF = DWT/tire radius
The propulsive force is equal to the drive wheel torque divided by the radius of the tires; the resultant is a force and no longer a torque because we have divided the torque by the distance at which it is applied to the road
4) NF = PF - RF
The net force acting on the vehicle is equal to the propulsive force subtracted from all resistive forces, which includes friction and wind resistance
5) A = NF/Mass
The acceleration of the vehicle is equal to the net force acting on the vehicle divided by its mass
The concept is understandably confusing at this point, as you may be thinking that horsepower has no relationship to acceleration and torque alone is responsible. However, don't forget that horsepower and torque are related - we could easily calculate the rate of acceleration from horsepower, we'd simply have to convert our horsepower into torque at the given RPM prior to plugging into the equations above. Also keep in mind that this process calculates acceleration at a particular point in time; the rate of acceleration is constantly changing with engine speed.
You might also stumble on the fact that torque is directly related to acceleration, yet you can apply a torque with no movement. Remember, acceleration is related to the net force acting on the vehicle, not the propulsive force alone. If the net force is zero, the rate of acceleration must be zero. A vehicle moving at constant speed experiences no acceleration because the forces acting against the vehicle are equal to the driving force of the vehicle. Therefore, the net force acting on the vehicle is zero.
Diesel owners tend to pay particular attention to the torque ratings of an engine more so than the peak horsepower an engine can produce. In the grand scheme of things, both are of equal importance. An engine producing greater torque will have the greater ability to overcome large loads from a standstill - accelerating a heavy trailer up to speed from a dead stop, for example. Likewise, greater horsepower potential translates into the ability to keep a heavier object moving at a constant speed.
It's important to realize that manufacturer's advertise peak engine horsepower and torque. That is, the maximum horsepower and torque that an engine can produce. Peak horsepower/torque are only realized under wide open throttle driving conditions, whereas the actual engine horsepower and torque being produced under given circumstances depends on the total load applied to the engine. A vehicle towing a 10,000 pound trailer will need to produce more power (and therefore greater throttle input) than a vehicle towing a 5,000 pound trailer in order to maintain a given speed. Load is also an important principle - if you were to rev an engine at full throttle with the transmission in neutral, it would produce very little torque as the only load applied to the engine would result from the mass of the rotating assembly. However, if you place the transmission in drive and accelerate from a standstill at wide open throttle, the engine load will be high and it will eventually produce peak torque followed by peak horsepower at the corresponding engine speeds.
In the end, torque and horsepower are of equal importance and inherent value in understanding the performance characteristics of internal combustion engines. Don't get hung up trying to put your finger on the differences between horsepower and torque - it is the relationship between the two that is important.