Notice that the additional drag of the gondola, fins, and rigging can be substantial. For example, Hörner gives the drag coefficient of an airship at zero angle of attack as = 0.023 for the hull alone and for the complete airship, including nacelles, fins, etc. Recall that the drag on an airship is mostly from boundary layer shear stress or skin friction over the large surface area of the gas envelope. A larger airship with a higher Reynolds number at the same airspeed will have a lower drag coefficient. Therefore, its drag, being proportional to the wetted surface, grows with less than the square of the increase in the length scale, while the aerostatic lift is proportional to the cube of the length scale.

# Power Required for Flight

To propel an airship, its aerodynamic drag must be overcome by the thrust from the propulsion system, i.e., the engines and propellers or fans. Estimates of the power required for the flight of an airship proceed along similar lines to that of the propeller-driven airplane. In the simplest terms, the maximum speed of an airship occurs when the maximum thrust generated by its engines is equal to the drag it experiences while being pushed through the air at that speed. That drag depends on the diameter and length of the airship, and more specifically, the projected frontal area and the total “wetted area” of its entire outer envelope. In general, the drag varies with the *square* of the airspeed, and so the power increases with the *cube* of the airspeed.

## Analysis

The drag in level flight is given by the conventional formula, i.e.,

(41)

where in this case the reference area on which is based is , so

(42)

Using Eq. 38, the drag coefficient can be expressed as

(43)

where from Eq. 37 the lift coefficient is

(44)

The corresponding power required for flight can be written as

(45)

where can be considered as the net efficiency of the propulsive system (engine and propeller combined); notice that this value may vary with airspeed.

Check Your Understanding #4 – Estimating forward flight power for an airship

An airship with a slenderness ratio of 3.9 has a buoyant gas volume of 6,600 m^{3} and cruises at an airspeed of 54.5 kts (28 m/s) at MSL ISA conditions using no dynamic lift. The drag coefficient on the airship based on Eq 31 is 0.051, and the propulsive efficiency is 0.80. Estimate the power required for flight.

## Show solution/hide solution.

The power required for flight can be written as

(46)

Inserting the values gives

(47)

which is about 149 shp ( 112 kW).