forces acting on the aircraft during a glide
our thanks (Copyright John Brandon)

In a gliding descent the forces are as shown in the diagram on the left. In the case of a constant rate descent the weight is exactly balanced by the resultant force of lift and drag. From the dashed parallelogram of forces shown it can be seen that the tangent of the angle of glide equals drag/lift.

For example assuming a glide angle of 10°, from the abridged trigonometrical table the tangent of 10° is 0.176, so the ratio of drag/lift in this case is then 1 : 5.7. (A little more accurate than using the '1-in-60' rule but inconsequential anyway.)

Conversely we can say that the angle of glide is dependent on the ratio of lift/drag at the airspeed being flown and the lower that ratio is then the greater the glide angle and consequently the greater the rate of sink and the lesser the distance the aircraft will glide from a given height. The rate of sink is the resultant of the gliding angle and the airspeed.

Be aware that the aircraft manufacturer's quoted L/Dmax may be overstated and will not take into account the considerable drag generated by a windmilling propeller [see below] so, for glide ratio purposes, it might be advisable to discount the quoted L/Dmax by maybe 20%. But the best option is to check it yourself.

Abridged trigonometrical table

Relationship between an angle within a right angle triangle and the sides:

Tangent of angle=opposite side/adjacent
Sine of angle=opposite/hypotenuse
Cosine of angle=adjacent/hypotenuse

Degrees Sine Cosine Tangent    Degrees Sine Cosine Tangent
1 0.017 0.999 0.017    50 0.766 0.643 1.192
5 0.087 0.996 0.087    55 0.819 0.574 1.428
10 0.173 0.985 0.176    60 0.866 0.500 1.732
15 0.259 0.966 0.268    65 0.910 0.423 2.145
20 0.342 0.939 0.364    70 0.939 0.342 2.747
30 0.500 0.866 0.577    75 0.966 0.259 3.732
40 0.643 0.766 0.839    80 0.985 0.173 5.672
45 0.707 0.707 1.000    90 1.000 0 infinity

The aoa associated with maximum L/D decides the best engine-off glide speed (Vbg) according to the operating weight of the aircraft. There are two glide speeds that the pilot must know and – more importantly – be familiar with the aircraft attitude associated with those airspeeds so that when the engine fails you can immediately assume [and continue to hold] the glide attitude without more than occasional reference to the ASI:

     •  Vmd – the minimum descent – the speed that results in the lowest rate of sink in a power-off glide, providing the longest time in the air from the potential energy of height. The lowest rate of sink occurs at the minimum value of drag Ũ velocity and, as stated above, may be around 90% of Vbg. Vmd is the airspeed used by gliders when utilising the atmospheric uplift from thermals or waves. This is the airspeed to select should you be very close to a favourable landing site with ample height and a few more seconds in the air to sort things out would be welcome.

Vmd decreases as the aircraft weight decreases from MTOW and the percentage reduction in Vmd is half the percentage reduction in weight. i.e. If weight is 10% below MTOW then Vmd is reduced by 5%. Vbg is also reduced in the same way if weight is less than MTOW.

     •  Vbg – the best power-off glide – the CAS that provides minimum drag thus maximum L/D, or glide ratio, consequently greatest straight line flight [i.e. air] distance available from the potential energy of height. The ratio of airspeed to rate of sink is about the same as the L/D ratio, so if Vbg is 50 knots [5 000 feet per minute] and L/Dmax is 7 then the rate of sink is about 700 fpm.

 This 'speed polar' diagram is a representative plot of the relationship between rate of sink and airspeed when gliding. Vmd is at the highest point of the curve. Vbg is ascertained by drawing the red line from the zero coordinate intersection tangential to the curve, Vbg is directly above the point of contact. Stall point is shown at Vs1.

Much is said about the importance of maintaining the 'best gliding speed' but what is important is to maintain an optimum glide speed; a penetration speed which takes atmospheric conditions into account, for example sinking air or a headwind. The gliding community refers to this as the speed to fly. The normal recommendation for countering a headwind is to add half the estimated wind speed to Vbg which increases the rate of sink but also increases the ground speed. For a tailwind deduct half the estimated wind speed from Vbg which will reduce both the rate of sink and the groundspeed. Bear in mind that it is better to err towards higher rather than lower airspeeds.

To illustrate this the polar curve on the left indicates the optimum glide speed when adjusted for headwind, tailwind or sinking air. For a tailwind the starting point on the horizontal scale has been moved a distance to the left corresponding to the tailwind velocity, consequently the green tangential line contacts the curve at an optimal glide speed which is lower than Vbg with a slightly lower rate of sink. The opposite for a headwind – purple line. For sinking air the starting point on the vertical scale has been moved up a distance corresponding to the vertical velocity of the air and consequently the pink tangential line contacts the curve at a glide speed higher than Vbg.

effect of a windmilling propeller

Both Vbg distance and Vmd time are adversely affected by the extra drag of a windmilling propeller, which creates much more drag than a stopped propeller following engine shut-down. If the forward speed is increased windmilling will increase, if forward speed is decreased windmilling will decrease, thus the windmilling may be stopped by temporarily reducing airspeed so that the negative lift is decreased to the point where internal engine friction will stop rotation.

However do not attempt to halt a windmilling propeller unless you have ample height and stopping it will make a significant difference to the distance covered in the glide. Sometimes it may not be possible to stop the windmilling.

practical glide ratio and terrain footprint

You should measure [preferably by stop watch and altimeter] the actual rate of sink achieved at Vbg with the throttle closed [engine idling], and from that you can calculate the practical glide ratio for your aircraft. The practical glide ratio is Vbg [in knots multiplied by 100 to convert to feet per minute] divided by the rate of sink [measured in fpm]. For example glide ratio when Vbg 60 knots, actual rate of sink 750 fpm = 60 Ũ 100/750 = 8, thus in still air that aircraft might glide for a straight line distance of 8000 feet for each 1000 feet of height.

These measurements should be taken at MTOW and then, if a two-seater, at the one person-on-board [POB] weight with the reduced Vbg.

The airspeed used should really be the TAS but, if the ASI is known to be reasonably accurate, using IAS will err on the side of caution, also with the engine idling a fixed pitch propeller will probably be producing drag rather than thrust so that too will be closer to the effect of a windmilling propeller. You should also confirm the rate[s] of sink at Vmd.

Having established the rates of sink you then know the maximum airborne time available. For example if the rate of sink at Vbg with one POB is 500 fpm and the engine fails at 1500 feet agl then the absolute maximum airborne time available is three minutes. If failure occurs at 250 feet whilst climbing then time to impact is 30 seconds, but 3 or 4 seconds might elapse before reaction occurs plus 4 or 5 seconds might be needed to establish at the safe glide speed. Read the section on conserving energy in the Flight Theory Guide.

Following engine failure it is important to be able to judge the available radius of action i.e. the maximum glide distance in any direction. This distance is dependent on the following factors, each of which involves a considerable degree of uncertainty:

the practical glide ratio
the topography [e.g. limited directional choice within a valley]
the height above suitable landing areas
turbulence, eddies and downflow conditions
manoeuvring requirements
and the average wind velocity between current height and the ground.

The footprint is shifted downwind i.e. the into-wind radius of action will be reduced while the downwind radius will be increased. The wind velocity is going to have a greater effect on an aircraft whose Vbg is 45 knots than on another whose Vbg is 65 knots. Atmospheric turbulence, eddies and downflows will all contribute to loss of height. Rising air might reduce the rate of descent.

Considering the uncertainties involved [not least being the pilot's ability to judge distance] and particularly should the engine fail at lower heights where time is in short supply, it may be valid to just consider the radius of the footprint as twice the current height – which would encompass all the terrain within a 120° cone and include some allowance for manoeuvring. The cone encompasses all the area contained within a sight line 30° below the horizon. If you extend your arm and fully spread the fingers and thumb the angular distance between the tips of thumb and little finger is about 20°. There is a drawback in that total area available from which to select a landing site is considerably reduced; the area encompassed within a radius of 60% of the theoretical glide distance is only about one third of the total area.

For powered chutes the radius of the footprint might be equivalent to the current height providing a 90° cone from a sight line 45° below the horizon.

Know the height lost during manoeuvres

Any manoeuvring involved in changing direction/s will occasion an increased loss of height and thus reduce the footprint. This reduction will be insignificant when high but may be highly significant when low. The increase in height loss during a gliding turn is, of course, dependent on the angle of bank used and the duration of the turn. Properly executed, gently banked turns which only change the heading 15° or so produce slight additional height loss [in fpm terms] and a slight reduction in the margin between Vbg and stalling speed, steeply banked turns through 210° will produce significant additional height loss and a major reduction in the margin between Vbg and stalling speed. You should be very aware of the height loss in 30°, 45° and 60° changes of heading because they are representative of the most likely turns executed at low levels.

Just because an aircraft has a good glide ratio does not mean it will perform equally well in a turn, it may lose more height in a turn than an aircraft which has a poorer glide ratio. For example a nice slippery aircraft with a glide ratio of 15 may lose 1000 feet in a 210° turn, whereas a draggy aircraft with a glide ratio of only 8 might lose only 600 feet in a 210° turn. Of course the radius of turn is greater in the faster, slippery aircraft.

Steepening the final descent path

If it is necessary to steepen the descent path to make it into a clearing the use of full flaps and/or a full sideslip, a sideslipping turn from base or careful fishtailing is usually recommended. A series of 'S' turns will reduce the forward travel. These techniques are certainly not something tried out for the first time in an actual emergency, they should only be used after adequate instruction and adequate competency has been reached – and maintained. The use of full flaps plus full sideslip may be frowned upon by the aircraft manufacturer but in an emergency situation use everything available.

height loss in a turn-back

When the engine fails soon after take-off the conventional and long proven wisdom is to, more or less, land straight ahead, provided that course of action is not going to affect others on the ground – for example put you into a group of buildings. If the engine fails well into the climb-out one of the possible options is to turn back and land on the departure field. If the take-off and climb was into-wind and a height of perhaps 1500 feet agl had been attained [and the rate of sink is significantly less than the rate of climb] then there would be every reason to turn back and land on that perfectly good airfield. There might be sufficient height in hand to manoeuvre for a crosswind rather than downwind landing.

On the other hand there will be a minimum safe height below which a 'turn-back' for a landing in any direction could clearly not be accomplished. To judge whether a safe turn-back is feasible the pilot must know the air radius of turn and how much height will be lost during the turn-back in that particular aircraft in similar conditions, then double it for the minimum safe height. Such knowledge can only be gained by practising turn-backs at a safe height and measuring the height loss.

Radius of turn and height loss

In a turn-back to land on the departure runway it is important to minimise both the distance the aircraft moves away from the extended line of the runway and the time spent in the turn. The slowest possible speed and the steepest possible bank angle will provide both the smallest radius and the fastest rate of turn, however these advantages will be more than offset by the following:

When the steepest bank angle and slowest speed is applied the necessary centripetal force for the turn is provided by the extra lift gained by increasing the angle of attack ( or CL) to a very high value. Also due to the lower velocity a larger portion of the total lift is provided by CL rather than Vē. Consequently the induced drag will increase substantially.

When turning it is not L/D that determines glide performance but rather the ratio to the drag of the vertical component of lift [Lvc] which offsets the normal 1g weight, or Lvc /D, and thus, due to the increase in induced drag, Lvc /D will be less than normal L/D resulting in an increase in the rate of sink and a steeper glide path. Lvc /D degrades as bank angle in the turn increases.

The stall speed increases with bank angle, or more correctly with wing loading, thus the lowest possible flight speed increases as bank in a gliding turn increases.

Any mishandling or turbulence during turns at high bank angles, near the accelerated stall speed, may result in a violent wing and nose drop with substantial loss of height.

Choosing the bank angle

In some faster aircraft it might be found that the turn back requires a steep turn, entered at a safe airspeed [ say 1.2 Ũ Vsturn ], where the wings are slightly unloaded by allowing the nose to lower a little further throughout the turn then, having levelled the wings, converting any airspeed gained into altitude by holding back pressure until the airspeed again drops to the target glide speed, not forgetting to allow for the ASI instrument lag. The bank angle usually recommended is 45° because at that angle the lift force generated by the wing is equally distributed between weight and centripetal force although the Vsturn will be increased to about 1.2 Ũ Vs1. Thus the safe airspeed would be 1.2 Ũ 1.2 Ũ Vs1 = 1.44 Vs1. [1.5 Vs1 is usually accepted as a "safe speed near the ground" for gentle manoeuvres]. If the aircraft has a high wing loading the sink rate in a steep turn may be excessive. Refer turn forces and bank angle.

For aircraft at the lower end of the performance spectrum it may be found that a 20° to 25° bank angle provides a good compromise with an appreciable direction change and a reasonable sink rate. There may be other techniques for an aircraft fitted with high lift devices. All of which indicates that performance will vary widely and you must know your aircraft and establish its safe turn-back performance under varying conditions otherwise never turn back!

Canadian statistics indicate
"if an engine failure after takeoff results in an accident, the pilot is at least eight times more likely to be killed or seriously injured turning back than landing straight ahead."