Propulsion (physics)

The propulsion is in the drive technology (also as a driving force ;) and related issues like biomechanics the force , which serves locomotion. The reaction force of the driving force in vehicles z. B. by wheels, in living beings by extremities, such as wings or fins , transmitted to the environment. Propulsion is only possible through recoil in a vacuum.

In order to generate propulsion, an energy source, an energy converter and an element for power transmission are usually required. Simpler examples are the direct use of gravitational force or wind power for the drive.

Land vehicles

Road vehicles

Road vehicles are exposed to different resistances , which have to be compensated by propulsion: For example the air resistance , the gradient resistance , the acceleration resistance or the rolling resistance of the wheels. The friction losses within the vehicle between the drive engine and the driven wheels are added to the efficiency of the drive machinery (bearing friction resistances, engine and gearbox resistances ), and the vehicle is divided into the drive and output sides , of which only the latter is considered here.

The air resistance can be calculated from:

${\displaystyle F_{\mathrm {WL} }={\frac {\rho }{2}}\,c_{w}\,A\,v^{2}}$

${\displaystyle \rho }$: Air density , 1.4 ... 1.2 kg / m³ (−20 ° C to +30 ° C)

${\displaystyle c_{w}}$: Drag coefficient

${\displaystyle A}$: Face

${\displaystyle v}$: Approach velocity

The air resistance increases with the square of the speed.

• ${\displaystyle c_{w}}$is 0.6 for a convertible and around 0.25 for a modern car, the old VW Beetle had 0.42, 0.7 for a flatbed truck and 1.1 for a semitrailer.
• The frontal area is approx. 2 m² for cars, 10 m² for a truck (4 m × 2.55 m according to StVO), and for rail vehicles 10–15 m² (European standard: 4.30 m × 3.25 m maximum ).
• The rolling resistance is calculated from the rolling resistance coefficient c _Ro of 0.001 for railways and about 0.006-0.015 for car tires on asphalt, is around 1% for rail vehicles and cars, but typically reaches 3–5% on bad roads, and significantly more for commercial vehicles.

Other resistances include cornering resistance and water resistance in wet conditions, which is speed-dependent (see aquaplaning ) and others.

Overall, the vehicle resistance is around 14% for a 40 t articulated truck loaded at 80 km / h, and unloaded at 31%.

The propulsion that makes the movement possible is usually transmitted by wheels or tracks , which can only be achieved through slip . Too much slip has a negative effect on driving stability. Modern vehicles therefore have control systems that limit propulsion.

With record-breaking vehicles , the required power can no longer be transferred to the road; the propulsion then has to be generated by jet engines. Other possibilities for generating propulsion are draft animals, muscle strength, or weight .

Rail vehicles

The total ground resistance is , however, quite relevant for rail vehicles with a rigid axle, no steering and the low static friction of steel on steel when cornering (arc resistance or resistance to curvature). Both partial resistances are quite independent of the speed, but proportional to the weight of the vehicle. Another resistance is the pitch resistance.

The ground resistance is caused by rolling friction and the executives and is composed of the frictional resistance between the wheel rim and track and the rolling resistance (the deformation resistance of the wheels or the rail). ${\displaystyle c_{\mathrm {Re} }}$ ${\displaystyle c_{\mathrm {Ro} }}$

Overall, the vehicle resistance is around 4% for a 1,800 t freight train (four-axle) at 80 km / h.

There is no rolling resistance on magnetic levitation trains. The propulsion is generated by linear motors and, compared to the wheel-rail system, is not limited by the frictional connection. This allows for greater gradients. Another way of overcoming steep gradients is the form-fitting connection between the toothed wheel and rack in rack railways .

Acceleration and performance

→ Main article : acceleration resistance

When accelerating a vehicle, not only the mass but also the rotating parts (engine, transmission, wheels) must be taken into account. The mass moments of inertia of the rotating parts are reduced to the drive axle. The result is a rotational drag force:

${\displaystyle F_{\mathrm {rot} }={\frac {\Theta _{\mathrm {rot} }}{r^{2}}}a}$

${\displaystyle \Theta _{\mathrm {rot} }}$: The moment of inertia of all rotating parts on the drive axis is reduced

${\displaystyle r}$: Radius of the wheel

This force is part of the vehicle's internal resistance and is therefore no longer available to accelerate the vehicle.

The total force required for acceleration results from the translational and rotational component:

${\displaystyle F_{B}=\left({\frac {\Theta _{\mathrm {rot} }}{r^{2}}}+m\right)\cdot a}$

${\displaystyle a}$: Acceleration

${\displaystyle m}$: Dimensions

The power required for a speed results from the sum of all resistances : ${\displaystyle P}$ ${\displaystyle F_{\mathrm {W} }}$

${\displaystyle P=F_{\mathrm {W} }\cdot v}$

The power depends on the speed in the third power, since the air resistance increases with the square of the speed. This is why the maximum speed depends so much on the drive power, and the ability to accelerate also decreases sharply with the square of the speed.

Aircraft

In aviation, only air resistance is important (except for take-off and landing). In flight, the direction of movement and propulsive force are generally in one line, and, because the flow velocity primarily depends on the airspeed, so is the resistance on the fuselage. The air resistance can be separated into a form drag , the more parasitic drag , and an induced drag caused by the lift. A large number of different aircraft propulsion systems have been developed to generate the required propulsion .

Lighter than air

• In the simplest case of a balloon, there is no propulsion force, the buoyancy is generated by displacement (static buoyancy) : The balloon travels wherever the wind blows and as fast as the wind blows (assuming a stable current), the movement over the ground only occurs through the movement of the medium.
• In an airship , the lift is also generated by the buoyancy body. For low speeds, the air resistance is calculated according to the linear law of resistance , i.e. it is proportional to the speed. The air resistance of an airship is less dependent on its frame surface (end face), but rather on its volume , i.e. on the ratio of length to diameter. Optimal values ​​are included . Propulsion is generated by propellers that can be pivoted to improve maneuverability. ${\displaystyle V}$ ${\displaystyle l/d\approx 4{,}5}$
  

Heavier than air

Forces on the wing in gliding flight

When flying with wings , the dynamic lift generated by the wings is the decisive factor. The drag acting on the wing is the total drag of the aircraft. In order to relate the resistance of the fuselage to the wing, by determining the balance of forces, one introduces a harmful area , the area of ​​a square plate (with a c _W value of 1.2) with the same resistance as the non-buoyant parts of the aircraft and is to be imagined mounted in the pressure point of the profile. This value is simply added to the wings.

• With gliders in stationary gliding , an equilibrium is established between the air resistance and the component of the weight force in the direction of flight, which provides the propulsion.
• In propeller-driven aircraft, the attitude corresponds to a glider flight with additional propulsion power. The same physical process takes place on the wings of the propeller as on the wings, only here the lift of the wings forms the drive (the screwing force ).

Forces on the plane

• With recoil propulsion, the propulsive force is called thrust .
  Shortly before reaching the sound barrier, the drag coefficient increases sharply, but decreases again in supersonic flight . In these areas, the Mach index ( speed through the speed of sound ) is an important parameter. The c _w -value rises to sometimes multiple values ​​and approaches a stable value again, which is close to the subsonic value. ${\displaystyle Ma=v/c}$ ${\displaystyle Ma\to 1}$ ${\displaystyle Ma>2}$

Spacecraft

The air resistance is lowest when the rocket has the shape of an elongated triangle, because it “rides” on the exhaust gas jet (which also expands laterally) and there is no suction resistance at the rear. Omnipotent wings usually only serve as flight stabilizers , which prevent the missile from rotating around its longitudinal axis or from starting to spin .

Propulsion is generated by rocket engines that are designed for use in a vacuum .

The propellant makes up a large part of the mass of the missile and therefore the mass cannot be considered constant. The basic rocket equation applies :

${\displaystyle F_{\mathrm {V} }=F_{\mathrm {P} }=v_{\mathrm {s} }\cdot {\frac {\mathrm {d} m}{\mathrm {d} t}}}$

v _s : jet speed of the engine

For space probes z. B. in the Voyager program , the gravity of other celestial bodies is used to accelerate (so-called " swing-by "), since the fuel on board would not be sufficient for such missions.

Watercraft

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• When swimming , the propulsion depends on the swimming style : the fastest style is the crawl .
• Muscle-powered boats use paddles or straps to transmit power to the water. With rafts also stakes to push off the ground.
• In yaw ferries , the energy of the flowing water is used for propulsion.
• Paddle steamers are driven by paddle wheels. Today these are mostly only used for tourist purposes.
• The field of propulsion of boats and ships is called "propulsion".

literature

• Karl-Heinrich Grote, Jörg Feldhusen (Hrsg.): Dubbel - paperback for mechanical engineering . , Springer, Berlin, various editions, currently: 22nd edition, 2007, ISBN 978-3-540-49714-1
• Manfred Mitschke: Dynamics of Motor Vehicles . Springer, Berlin 1972, 1982, ISBN 3-540-05207-0 , 2004, ISBN 978-3-540-42011-8
• Dietrich Wende: Driving dynamics. Transpress, Berlin 1983, 1990, ISBN 3-344-00363-1
• H. Oertel (ed.): Prandtl guide through fluid mechanics. Fundamentals and phenomena . Vieweg, 2002 (11th edition), ISBN 3-528-48209-5

Individual evidence

1. ^ Automotive paperback . 22nd edition. Springer, 1998, ISBN 978-3-662-22073-3 ( limited preview in Google book search).
2. ↑ ^{a b} Dubbel, chap. Resistance of vehicles
3. ↑ ^{a b} Rainer Rauschenberg: Potentials for reducing the external effects of the transport sector through decentralized and automated rail freight transport . Dissertation, Department of Economics, Goethe University, Frankfurt am Main; especially chap. 4: Technical influencing variables ( web document ), total November 27, 2007
4. ↑ ^{a b} Mitschke, 1972, p. 39ff - after Rauschenberg
5. ↑ Reif (ed.): Driving stabilization systems and driver assistance systems . 1st edition. Springer, 2010, ISBN 978-3-8348-1314-5 ( limited preview in Google book search).
6. ↑ Wende, 1983, p. 36ff - after Rauschenberg
7. ↑ Dubbel, 7th edition, p. 272, Fig. 69