Some relationships between torque and power

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Power: What is power? Power is a physical quantity that indicates the speed at which an object performs work. In physics, power P is defined as work W divided by time t, and its unit is the watt, denoted as W. Common units of power that we see in the media include kW, PS, HP, BHP, WHP, etc.; there was also the CV unit used in Italy in the past. Among these, the kilowatt is the international standard unit, with 1 kW equal to 1000 W – that is, if 1000 joules of work are done in 1 second, the power is 1 kW. In daily life, we often refer to power colloquially as horsepower, with the unit being horsepower, just as torque is called twisting force. In a car, the main power-generating component is the engine. The power of the engine is calculated based on torque, and the formula for this calculation is quite simple: Power (W) = 2π × Torque (Nm) × Rotational speed (rpm) / 60. Simplified, this becomes: Power (kW) = Torque (Nm) × Rotational speed (rpm) / 9549. However, how is power in kw converted into the horsepower value that is commonly used? Due to the differences between imperial and metric systems, the definition of horsepower is essentially different. The British unit of horsepower (hp) is defined as the amount of work done by one horse in pulling an object weighing 200 pounds over a distance of 165 feet in one minute; this amounts to 33,000 lb-ft/min ； The metric definition of horsepower (ps) is one horse pulling a 75 kg object 60 meters in one minute; when these values are multiplied, the result is 4500 kgm/min. After performing the unit conversions (1 lb = 0.454 kg; 1 ft = 0.3048 m), it was found that 1 hp equals 4566 kgm/min, which differs slightly from the metric value of 1 PS equaling 4500 kgm/min. When converting using watts as the unit (1 W = 1 Nm/sec = 9.8 kgm/sec), we get 1 hp = 746 W and 1 PS = 735 W; these two values differ by about 1.5%. Why on earth are there two systems in the world, imperial and metric? It’s just like why some cars have right-hand steering while others have left-hand steering – differences that humanity can never reconcile. If we look at some of the more well-known testing standards, Germany’s DIN and the European Community’s new standard EEC, as well as Japan’s JIS, use the metric unit ps to express horsepower, while SAE uses the imperial unit hp. However, with the advent of an integrated global economy and to avoid complicated conversions, more and more manufacturer specifications now provide the internationally accepted unit of kilowatt kW to indicate engine power output. Summary: 1 hp = 0.746 kW, 1 PS = 0.735 kW, and 1 hp = 1.014966 PS. The calculation of gross horsepower differs from that using hp; WHP and BHP are power units based on hp but measured using different methods – namely wheel horsepower and brake horsepower. WHP represents the power output of the wheels as measured by a dyno (commonly known as a power testing device), while BHP is the power value measured from the engine shaft, taking into account accessories such as the generator and water pump. The difference between BHP and hp is very small. Torque: In physics, torque refers to the magnitude of a moment, and it is equal to the product of force and the lever arm. Its international unit is the newton-meter (Nm). Additionally, torque can be expressed in units such as kgm and lb-ft. Since G = mg, when g = 9.8, 1 kg = 9.8 N; therefore, 1 kgm = 9.8 Nm. The pound-foot (lb-ft) is a unit of torque used in the imperial system. With 1 lb = 0.4536 kg and 1 ft = 0.3048 m, it can be calculated that 1 lb-ft = 0.13826 kgm. In everyday language, torque is often referred to as twist force (which are two different concepts in physics). Let’s take an example: the 8th-generation Civic 1.8 has a torque of 173.5 Nm at 4300 rpm, which means that the engine generates 173.5 Nm of torque at 4300 revolutions per minute. So how can a force of 173.5 Nm be enough to make a car weighing over 1 ton move? In fact, the torque generated by the engine needs to be amplified (at the cost of reducing the rotational speed), and this is achieved through the gearbox, final drive, and tires. The torque generated by the engine first passes through the gearbox, where it is \"adjustably\" amplified (or reduced in overdrive mode), before being sent to the final drive gearset for further amplification (while the engine speed decreases further). Finally, the driving force is delivered through the tires. If the gear ratio of first gear in a vehicle is 3 (the ratio of the number of teeth on the gears, which is essentially the ratio of their radii), the final gear ratio is 4, the tire radius is 0.3 meters, and the original torque is 200 Nm, then the torque at the axle will be 200×3×4 = 2400 Nm (assuming a 100% transmission efficiency). By dividing this value by the tire radius of 0.3 meters, the driving force generated due to friction between the tires and the ground is 2400 Nm/0.3 m = 8000 N, which is sufficient to propel the vehicle. 　　When it comes to mechanical efficiency, there is a loss of power with each gear shift; the mechanical efficiency of a manual transmission is around 95%, while that of an automatic transmission is lower, at about 88%. The efficiency of the universal joints in the drive shaft is approximately 98%. Overall, the driving force of a vehicle can be calculated using the following formula: Torque × Gear ratio of the transmission × Final gear ratio × Mechanical efficiency. Driving force = ———————————————————— Tire radius (in meters). Summary: 1 kgm = 9.8 Nm; 1 lb-ft = 0.13826 kgm; 1 lb-ft = 1.355 Nm. Generally speaking, when the engine displacement remains constant, cylinders with a smaller bore and a longer stroke produce more torque, with lower rotational speeds, making them suitable for vehicles that require high loads. Cylinders with a large bore and short stroke place more emphasis on power output, typically have higher rotational speeds, and are suitable for vehicles designed for high speed. In simple terms: Power is proportional to torque times rotational speed. As a supplementary point: Why can an engine’s power be calculated from torque? We know that power P = work W ÷ time t, and work W = force F × distance s. Therefore, P = F × s/t = F × velocity v. Here, v is the linear velocity; in an engine, the linear velocity of the crankshaft equals the angular velocity ω of the crankshaft multiplied by the radius r of the crankshaft. Substituting this into the formula gives: Power P = force F × radius r × angular velocity ω ； And since Force F × radius r = torque, it follows that Power P = torque × angular velocity ω. Therefore, the power of an engine can be calculated from torque and rotational speed. The unit of angular velocity is radians per second; in the radial system, pi represents 180 degrees