What is the definition of the drag coefficient

Air resistance

Lexicon> Letter L> Air resistance

Definition: the friction that arises when a body moves through the air

English: air drag

Categories: Vehicles, Basic Terms, Physical Basics

Author: Dr. Rüdiger Paschotta

How to quote; suggest additional literature

Original creation: 09/26/2014; last change: 21.09.2020

URL: https://www.energie-lexikon.info/luftverbindungen.html

When a body, such as a vehicle, moves through the air, it creates friction. The air is partly carried away by the vehicle and set in motion, with turbulent currents also occurring at higher speeds. This results in a loss of energy, which is related to the resulting frictional force. (The energy loss is equal to the frictional force multiplied by the distance the body is moved.) This type of friction is known as drag (or more generally drag). With a moving vehicle, these aerodynamic forces have to generate correspondingly more drive power in order to maintain the speed.

In cars and other motor vehicles, the air resistance is the dominant part of the frictional forces (and usually a substantial part of the total driving resistance) as long as the driving speed is not very low (e.g. below 30 km / h). At very low speeds, on the other hand, rolling resistance dominates.

Strength of drag force

The strength of the drag force in the case of a turbulent flow (i.e. at not very low speeds) is given by the following formula:

So it depends on several factors:

  • the drag coefficient (cW.Value) of the body
  • from the cross-sectional area (frontal area) A. of the moving body in the direction of travel
  • the density ρ of the air (which decreases significantly at high altitudes, for example the flight altitude of an airplane)
  • from the square of the speed v (more precisely the relative speed between the body and the ambient air)

The drag force is therefore proportional to the mentioned cross-sectional area and also to the drag coefficient (cW.Value), which depends on the geometric shape of the body. This means that a streamlined shape z. B. a vehicle with a given cross-sectional area reduces the drag. However, if the cW.- If the cross-sectional area is increased (e.g. to enlarge the interior space), the air resistance also increases again.

If the vehicle is moved against a wind coming from the front (headwind), the relevant relative speed increases by the wind speed. The additional frictional force caused by the wind, because of the quadratic dependence on the relative speed, is all the more significant the faster the vehicle moves.

Optimizing the shape of a vehicle for the lowest possible cW.-Value is a very difficult task. Mathematically, the cW.-Calculate the value relatively easily only for very simple shapes; for vehicles one needs highly complicated approximate calculations with powerful computers or experimental measurements in the wind tunnel. The effect of changes in shape, for example by attaching spoilers, can only be roughly estimated without such effort.

The air resistance depends very much on the speed of a vehicle.

At the typical speeds of vehicles, turbulent air currents arise, for which the above formula applies and the drag force is proportional to the square of the speed. This means that at twice the speed, four times the frictional force arises, so that the necessary drive power (as far as it is due to the air resistance) is eight times higher. (The drive power is the product of power and speed.) This explains why low-powered vehicles do not have as much lower top speeds as one might expect, while even extreme sports cars with 1000 hp are only around twice as fast as one ordinary car. The drive energy expenditure per kilometer traveled (insofar as it is caused by air resistance) increases fourfold when the speed is doubled. Since the efficiency of the internal combustion engine of a car decreases at low speeds and the rolling resistance does not increase at high speeds, the dependence of the fuel consumption on the driving speed is somewhat less strong than would be expected from the above.

When a car is driven with the windows open, it creates significantly more drag. This means that operating an air conditioning system is usually more energetic than driving with the windows open, except at very low speeds.

At very low speeds, laminar (non-turbulent) flows occur, with the frictional force being proportional to the speed. However, this regime is not relevant for vehicles, since the rolling resistance that is approximately independent of the speed dominates in this speed range.

Numerical example: VW Golf

As a numerical example, consider a VW Golf VII with a frontal area of ​​2.19 m2 and a cW.Value of 0.27. Figure 1 shows the drag force as a function of speed.

Even the best technology will hardly make it possible to drive very economically at high speeds.

At 100 km / h there is a force of 274 N (Newtons). Multiplied by the driving speed of 100 km / h = 27.8 m / s, this results in a drive power of 7.6 kW. The consumption of drive energy (only for overcoming air resistance) is then 7.6 kWh per 100 km. If the drive system (motor, gearbox, etc.) provides this drive energy with an efficiency of 25% (roughly estimated), you need 30.4 kWh of primary energy per 100 km, which corresponds to approx. 3.6 liters of petrol. At 150 km / h it would be 8.1 l. It can be seen that a fuel consumption of a few liters per 100 kilometers at 100 km / h is technically easy to achieve with an efficient drive, but is practically impossible at high motorway speeds.

Optimization of the cW.Values ​​of cars

In the 1950s, cW.-Values ​​in the region of 0.5 normal. At that time, the shape of the body of most cars was not optimized for low air resistance, but rather determined by fashion, practical or manufacturing aspects. Meanwhile the cW.-Values ​​of most new vehicles in the area of ​​0.25 to 0.35. The noticeably very significant improvement was achieved through a variety of measures, in particular through a more “streamlined” shape of the body, but also through carefully optimized components such as rear diffusers, a relatively smooth underbody and optimized attachments (e.g. rearview mirror).

Further improvements would certainly be possible, but would often come into conflict with other design goals. For example, all-round visibility can be impaired by windows that are less high and rather flat, and the cooling of the engine is reduced if the air flow through the engine compartment is reduced. (The latter factor is of course more important with particularly powerful and inefficient engines.) Because of such compromises, the cW.Values ​​of cars will be well below 0.25 in the future. This means that a further reduction in energy losses due to air resistance is only possible with two measures: by reducing the cross-sectional area and, above all, by reducing driving speeds (especially on motorways).

Parasitic and induced drag in aircraft

The generation of dynamic lift goes hand in hand with additional air resistance.

At first glance, one would expect for aircraft as well as for land vehicles that the drag force would increase rapidly with increasing speed (here: speed against the surrounding air). However, this only applies to the so-called parasitic resistance, which is created similarly to a typical land vehicle. Another aspect also plays an important role here, namely that the wings in particular have to generate dynamic lift in order to keep the aircraft in the air. The generation of this necessary lift goes hand in hand with the fact that additional air resistance (the so-called induced drag) arises. Its strength does not increase with increasing speed, but rather decreases significantly.

If you consider the air resistance as a function of the airspeed, it makes sense to assume straight flight at constant altitude at any speed. So regardless of the speed, the same dynamic lift must always be available. At low speeds, this must be ensured by a corresponding configuration of the aircraft, for example by increasing the angle of attack of the entire aircraft (nose more upwards) and / or by modifying the shape of the wings, for example by extending landing flaps. This then increases the induced drag.

At low flight speeds, the air resistance increases!

The total air resistance is now the sum of the parasitic drag and the induced drag. It turns out that it becomes minimal at a certain speed at which both contributions become roughly the same. At higher speeds, the parasitic drag predominates, at lower speeds the induced drag. In the case of extremely slow flight (e.g. when taking off and landing), the drive power required can even be considerably higher than at a higher flight speed.

If the efficiency of the drive (e.g. a jet engine) were independent of the speed, the mentioned speed of minimum air resistance would be optimal with regard to the fuel consumption per kilometer. However, since this is mostly not the case for jet engines in particular, the optimal flight speed is significantly higher - typically in the region of Mach 0.8, which corresponds to around 860 km / h at normal cruising altitudes. The cruising speed actually selected is often a little higher because it is a compromise between economy and flight duration.

The air resistance tends to decrease with increasing flight altitude, and the speed of minimum air resistance increases. This is mainly due to the decreasing density of the air.

Aerodynamic drag at supersonic speed

In the case of flights at supersonic speed, the dependence of the air resistance on the speed is modified again because additional, complicated aspects of aerodynamics then become relevant. When the speed of sound is reached or slightly exceeded, there is a sharp increase in air resistance, but when it is significantly higher, it drops again until another increase occurs. The local optimum in the supersonic range is, however, still significantly less favorable than a speed slightly below the speed of sound. Supersonic flight should therefore practically always lead to a significantly increased energy consumption.

Questions and comments from readers

29.03.2017

You write that even the best technology would not make it possible to drive economically at high speeds.

In my opinion, we are generally focusing too much on the automobile in its current form. In my opinion, the concept should be reconsidered.

How much energy would it require if vehicles were able to form columns to drive fast? Assuming an optimized shape, the air resistance would be almost identical to that of a single vehicle, since the frontal area is the same. How high would the expected energy expenditure be if, for example, 20 Golf-class vehicles were to be formed into a train in which the vehicles dock with one another, i.e. H. without distance?

I would be very interested in your opinion.

Answer from the author:

That would depend a lot on how smooth the column could be. If 20 vehicles in the shape of a VW Golf were to drive without a gap, there would certainly be much greater air resistance than for a single vehicle, mainly because the engine compartment is much less high than the passenger compartment. After all, it should be much better than when the vehicles drive at the usual distance from one another. Unfortunately, I cannot give a quantitative statement; this would require complex aerodynamic simulations, for example.

I fear that the proposed approach would be impractical. The effort would probably be enormous - far too high to be justified by moderate fuel savings. Only when most vehicles were equipped with the appropriate systems would many cars really be able to drive in appropriate columns on the autobahn.

I think other concepts are much more suitable - traveling by train for long distances and possibly a rental car (or car sharing) for the last few kilometers.

10.07.2017

The shape of the car has never been consistently optimized in terms of flow, as is the case, for example. B. is the case with aircraft. Most of the time, improvements were only sought to the given, familiar shape. If the form were to be optimized consistently in terms of flow technology, Cd values ​​of less than 0.1 would be possible without any problems. It would also be possible to have the front face at or even below 1 m2 without having to accept any loss of comfort or a lack of security. Together with a weight reduction and the latest tire technology with low rolling resistance, it would be absolutely possible to outbid today's cars in terms of their energy efficiency by a factor of 10. Which would then also bring the (still) limited range of electric vehicles to well over 1000 km per charge.

As mentioned, such vehicles would look more like an airplane, a fish, or a velomobile. The auto industry does not deny that it is possible to build such vehicles, but justifies not building that it cannot sell such vehicles. So the problem seems to be more of a psychological one. M. E. does not take this argument. In any case, I hardly know anyone who does not perceive an airplane or a dolphin as aesthetic, at best perhaps a little unfamiliar on the street. However, the energy advantages and thus also cost savings will soon make this aspect irrelevant.

Efforts are currently underway to mass-produce such a high-tech vehicle after years of private development (not on my part).

Answer from the author:

I fear that the concerns of the auto industry are not entirely unfounded, but at the same time I hope that you are right!

29.08.2018

Am I making a mistake? If I look at the right column “Drive power” in the diagram, then I see that with increasing speed, the necessary drive power does not grow with the square of the speed. At 80 km / h you need around 4 kW, at 160 km / h it is already 30 kW. So that is around a factor of 8 and therefore does not result in a factor of 22 but 23. How does this fit in with the fact that at twice the speed, the air resistance is quadrupled?

Answer from the author:

The drag force is quadrupled at twice the speed. However, the drive power is the product of force and speed, and that is why it increases by a factor of 8. So you need disproportionately more drive power for high driving speeds. This is why most cars have a top speed between 130 km / h and 200 km / h, although they differ much more in terms of engine performance.

The driveenergy for 100 km, however, it “only” quadruples, since you only need half as long at double the speed.

In practice, fuel consumption increases significantly less than fourfold, because firstly the air resistance is not the only problem and z. B. the consumption is independent of the speed due to the rolling resistance, and secondly, the efficiency of the engine may be slightly better with higher power. At really high speeds this is of little help, as the air resistance is very dominant and the engine may become more inefficient again (e.g. due to full load enrichment).

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See also: friction, power, energy loss, saving fuel, rolling resistance, driving resistance
as well as other articles in the categories vehicles, basic concepts, physical principles