Someone needs to calculate the power of the propulsion unit in order to calculate the car tax. It is important for some to independently calculate the power of the compressor engine. It is important for someone to know exactly the power of the machine in order to compare it with the one that was declared. In general, power calculation and engine selection are two inseparable processes.
These are not the only reasons why motorists are trying to independently calculate the power of the engines of their cars. This is quite difficult to do without the necessary formulas for the calculation. They will be given in this article so that every motorist can calculate for himself how much the real engine power of his car is.
Introduction
There are at least four common ways to calculate the power of an internal combustion engine. In these methods, the following parameters of the propulsion unit are used:
- Turnovers.
- Volume.
- Twistingmoment.
- Effective pressure inside the combustion chamber.
For calculations, you need to know the weight of the car, as well as the acceleration time to 100 km/h.
Each of the following formulas for calculating engine power has some error and cannot give a 100% accurate result. This should always be taken into account when analyzing the received data.
If you calculate the power using all the formulas that will be described in the article, you can find out the average value of the real motor power, and the discrepancy with the actual result will be no more than 10%.
If we do not take into account the various scientific subtleties associated with the definition of technical concepts, then we can say that power is the energy generated by the propulsion unit and converted into torque on the shaft. At the same time, power is a variable value, and its maximum value is achieved at a certain shaft rotation speed (indicated in the passport data).
In modern internal combustion engines, maximum power is achieved at 5, 5-6, 6 thousand revolutions per minute. It is observed at the highest average effective value of pressure in the cylinders. The value of this pressure depends on the following parameters:
- fuel mixture quality;
- Combustion completeness;
- fuel loss.
Power, as a physical quantity, is measured in Watts, while in the automotive industry it is measured in horsepower. The calculations described in the methods below will give results in kilowatts, then they will need to be converted to horsepower usingspecial calculator-converter.
Power Through Torque
One way to calculate the power is to determine the dependence of the motor torque on the number of revolutions.
Any moment in physics is the product of force on the shoulder of its application. Torque is the product of the force that the engine can develop to overcome the resistance of the load, by the shoulder of its application. It is this parameter that determines how quickly the motor reaches its maximum power.
Torque can be defined as the ratio of the product of the working volume and the average effective pressure in the combustion chamber to 0.12566 (constant):
- M=(Vworking Peffective)/0, 12566, where Vworking– engine displacement [l], Peffective – effective pressure in the combustion chamber [bar].
Engine speed characterizes the speed of rotation of the crankshaft.
Using engine torque and RPM values, the following engine power calculation formula can be used:
P=(Mn)/9549, where M is torque [Nm], n is shaft speed [rpm], 9549 is proportionality factor
Calculated power is measured in kilowatts. To convert the calculated value into horsepower, you need to multiply the result by a proportionality factor of 1, 36.
This method of calculation consists in using only two elementary formulas, therefore it is considered one of the simplest. True, you can do moreeasier and use the online calculator, in which you need to enter certain data about the car and its engine unit.
It is worth noting that this formula for calculating engine power allows you to calculate only the power that is obtained at the output of the engine, and not the one that actually comes to the wheels of the car. What is the difference? As long as the power (if you think of it as a flow) reaches the wheels, it experiences losses in the transfer case, for example. Secondary consumers like an air conditioner or a generator also play a significant role. It is impossible not to mention the losses to overcome the resistance to lifting, rolling, as well as aerodynamic resistance.
This disadvantage is partly offset by the use of other calculation formulas.
Power through Engine Size
It is not always possible to determine the engine torque. Sometimes car owners do not even know the value of this parameter. In this case, the power of the propulsion unit can be found using the volume of the motor.
To do this, you need to multiply the volume of the unit by the crankshaft speed, as well as by the average effective pressure. The resulting value must be divided by 120:
- P=(VnPefficient)/120 where V is engine displacement [cm3], n is speed crankshaft rotation [rpm], Peffective – average effective pressure [MPA], 120 – constant, proportionality factor.
This is how the engine power of a car is calculated withusing the unit volume.
Most often, the value of Peffective in gasoline engines of a standard sample varies from 0.82 MPa to 0.85 MPa, in forced engines - 0.9 MPa, and in diesel units the pressure value is between 0.9 MPa and 2.5 MPa.
When using this formula to calculate the real power of the motor, to convert kW to hp. s., it is necessary to divide the resulting value by a factor equal to 0, 735.
This calculation method is also far from the most complicated and takes a minimum of time and effort.
Using this method, you can calculate the power of the pump motor.
Power through air flow
The power of the unit can also be determined by the air flow. True, this calculation method is available only to those car owners who have an on-board computer installed that allows you to record air consumption at 5.5 thousand revolutions in third gear.
To get the approximate power of the engine, it is necessary to divide the consumption obtained under the above conditions by three. The formula looks like this:
P=G/3, where G is the air flow rate
This calculation characterizes the operation of the engine under ideal conditions, that is, without taking into account transmission losses, third-party consumers and aerodynamic drag. The real power is 10 or even 20% lower than the calculated one.
Accordingly, the amount of air flow is determined in the laboratory on a special stand on which the car is installed.
Readings of onboard sensors strongly depend on their pollutionand from calibration.
Therefore, calculating engine power based on air consumption data is far from the most accurate and effective, but it is quite suitable for obtaining approximate data.
Power through the mass of the car and acceleration time to "hundreds"
Calculation using the weight of the car and its acceleration speed to 100 km/h is one of the simplest methods for calculating the real power of the engine, because the weight of the car and the declared acceleration time to "hundreds" are the passport parameters of the car.
This method is relevant for engines running on any type of fuel - gasoline, diesel fuel, gas - because it takes into account only the acceleration dynamics.
When calculating it is necessary to take into account the weight of the vehicle together with the driver. Also, in order to bring the calculation result as close as possible to the real one, it is worth taking into account the losses spent on braking, slipping, as well as the reaction speed of the gearbox. The type of drive also plays a role. For example, front-wheel drive cars lose about 0.5 seconds at the start, rear-wheel drive cars from 0.3 seconds to 0.4 seconds.
It remains to find a calculator on the net to calculate the power of a car through acceleration speed, enter the necessary data and get an answer. It makes no sense to give the mathematical calculations that the calculator makes, because of their complexity.
The result of the calculation will be one of the most accurate, close to real.
This method of calculating the real power of a car is considered by many to be the most convenient, because car owners will have to make a minimum of effort - to measure the acceleration speed to100 km/h and enter additional data into the automatic calculator.
Other engine types
It's no secret that engines are used not only in cars, but also in industry and even in everyday life. Motors of various sizes can be found in factories - driving shafts - as well as in household appliances like automatic meat grinders.
Sometimes you need to calculate the real power of such engines. How to do this is described below.
It is worth noting right away that the calculation of the power of a 3-phase motor can be done as follows:
- P=Mtorquen, where Mtorque is torque and n is shaft speed.
Induction motor
Asynchronous unit is a device, the peculiarity of which is that the frequency of rotation of the magnetic field created by its stator is always greater than the frequency of rotation of its rotor.
The principle of operation of an asynchronous machine is similar to the principle of operation of a transformer. The laws of electromagnetic induction are applied (the time-varying flux linkage of the winding induces an EMF in it) and Ampere (an electromagnetic force acts on a conductor of a certain length, through which a current flows in a field with a certain value of induction).
Induction motor generally consists of a stator, rotor, shaft and support. The stator includes the following main components: winding, core, housing. The rotor consists of a core and a winding.
The main task of an induction motor is to transformelectrical energy, which is supplied to the stator winding, into mechanical energy, which can be removed from a rotating shaft.
Asynchronous motor power
In the technical field of science, there are three types of power:
- full (indicated by the letter S);
- active (indicated by the letter P);
- reactive (indicated by the letter Q).
Total power can be represented as a vector that has a real and an imaginary part (it is worth remembering the section of mathematics related to complex numbers).
The real part is the active power that is spent on doing useful work like rotating the shaft, as well as generating heat.
The imaginary part is expressed by the reactive power that takes part in the creation of the magnetic flux (indicated by the letter F).
It is the magnetic flux that underlies the principle of operation of an asynchronous unit, a synchronous motor, a DC machine, and a transformer.
Reactive power is used to charge capacitors, create a magnetic field around chokes.
Active power is calculated as the product of current and voltage and power factor:
P=IUcosφ
Reactive power is calculated as the product of current and voltage and power factor 90° out of phase. Otherwise, you can write:
Q=IUsinφ
The value of total power, if you remember that it can be represented as a vector,can be calculated using the Pythagorean theorem as the root sum of the squares of active and reactive power:
S=(P2+Q2)1/2.
If we calculate the total power formula in general form, it turns out that S is the product of current and voltage:
S=IU
Power factor cosφ is a value that is numerically equal to the ratio of the active component to the apparent power. To find sinφ, knowing cosφ, you need to calculate the value of φ in degrees and find its sine.
This is a standard motor power calculation based on current and voltage.
Calculation of the power of a 3-phase asynchronous unit
To calculate the useful power on the stator winding of an asynchronous 3-phase motor, multiply the phase voltage by the phase current and the power factor, and multiply the resulting power value by three (by the number of phases):
- Pstator=3UfIfcosφ.
Calculation of power el. of an active motor, that is, the power that is removed from the motor shaft, is produced as follows:
- Poutput=Pstator – Ploss.
The following losses occur in an induction motor:
- electrical in the stator winding;
- in stator core steel;
- electrical in the rotor winding;
- mechanical;
- additional.
To calculate the power of a three-phase motor in a stator winding with a reactivecharacter, it is necessary to add the three components of this type of power, namely:
- reactive power consumed to create the leakage flux of the stator winding;
- reactive power consumed to create the leakage flux of the rotor winding;
- reactive power used to create the main stream.
Reactive power in an asynchronous motor is mainly spent on creating an alternating electromagnetic field, but part of the power is spent on creating stray fluxes. Stray fluxes weaken the main magnetic flux and reduce the efficiency of the asynchronous unit.
Current power
Calculation of induction motor power can be done using current data. To do this, follow these steps:
- Power up the motor.
- Using an ammeter, measure the current in each turn.
- Calculate the average current value based on the results of measurements taken in the second paragraph.
- Multiply the average current by the voltage. Get power.
Power can always be calculated as the product of current and voltage. In this case, it is important to know which values of U and I should be taken. In this case, U is the supply voltage, it is a constant value, and I can vary depending on which winding (stator or rotor) the current is measured on, so it is necessary to choose its average value.
Power by size
The stator has many different components, one of which is the core. To calculate engine power withusing dimensions, do the following:
- Measure the length and diameter of the core.
- Calculate the constant C, which will be used in further calculations. C=(πDn)/(120f)
- Calculate the power P using the formula P=CD2ln10-6, where C is the calculated constant, D is the diameter of the core, n is the speed of rotation of the shaft, l is the length of the core.
It is better to make all measurements and calculations with maximum accuracy so that the calculation of the power of the electric drive motor is as close to reality as possible.
Tractive power
The power of an induction motor can also be determined using the value of the traction force. To do this, you will need to measure the radius of the core (the more accurate, the better), fix the speed at which the shaft of the unit rotates, and also measure the traction force of the engine using a dynamometer.
All data must be substituted into the following formula:
P=2πFnr, where F is the traction force, n is the shaft rotation speed, r is the core radius
Nuance of the induction motor
All of the above formulas, which are used to calculate the power of a three-phase motor, allow us to draw an important conclusion that motors can be of different sizes, have different speeds, but ultimately have the same power.
This allowsdesigners to create models of engines that can be used in a wide variety of conditions.
DC motor
A DC motor is a machine that converts electrical power received from direct current into mechanical power. The principle of its operation has little to do with an asynchronous machine.
A DC motor consists of a stator, armature and support, as well as contact brushes and a commutator.
Collector - a device that converts alternating current to direct current (and vice versa).
To calculate the useful power of such a unit, which is spent on performing any work, it is enough to multiply the armature EMF by the armature current:
- P=EaIa.
As you can see, the calculation of the power of a DC motor is much simpler than the calculations made in an asynchronous motor.
