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Decreasing your exposure to aerodynamic risk

6. The turn-back: possible or impossible
— or just unwise?

Rev. 4 — page content was last changed 17 June 2012

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Following engine failure after take-off [EFATO] there is a very strong compulsion to turn back to the safety of the airfield you have just left. That compulsion may be difficult to resist, particularly if hazardous terrain, rather than open fields, lies ahead. The question is should you or shouldn't you? 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." The words 'if ... results in an accident" signify that successful turn-backs are ignored in their statistics and this may also apply to turn-back statistics produced by other national authorities.

RA-Aus incident reports do record more than a few occasions where a pilot has achieved an injury-free and minimum damage landing following a turn-back or similar action, so successful turn-backs are certainly possible in very light sport and recreational aircraft.

But is a turn-back decision wise?


6.1 Why the high fatality rate?

Loss of control
The primary causal factor for the generally high fatality/severe injury rate is loss of control in a mistimed/poorly executed initial turn, perhaps being intimidated by terrain/obstructions; or, following a successful 180° turn, realising too late the airfield can't be reached resulting in an unplanned, perhaps desperate, reaction. The factors involved in loss of control events were discussed in the article 'Don't stall and spin in from a turn'.

Here's an extract from an RA-Aus accident report compiled by a qualified witness on behalf of the severely injured pilot. At the time, the pilot had a CPL and RA-Aus Pilot Certificate but only 2 hours experience in his Supercat CAO 95.10 aircraft. The crash occurred from a 900-metre runway at an airfield in mountainous terrain, at an elevation of 3300 feet. At the time, wind was light and variable with no turbulence, and temperature corresponded to the ISA norm. Apparently partial loss of thrust was experienced on take-off. " The aircraft took off normally ... climbed to 150–200 feet near the end of the runway ... then appeared to sink and turn left ... (there is a power line 300 m past the runway end, below runway level in a ravine) ... the angle of bank increased rapidly until it appeared to be almost 90°. The aircraft descended rapidly and disappeared behind some trees followed by a surprisingly soft 'crump'." The aircraft hit the ground almost vertically.

6.2 Opting for the turn-back

The need for a properly derived decision
The conventional and generally long-accepted wisdom in the event of a low-level off-field failure is for a properly controlled landing — hopefully into wind, more or less straight ahead, but certainly somewhere within 60° either side of the initial path. Factors involved were examined in the three preceding modules of this series.

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 less than the rate of climb) then there would be every reason to turn back and land on that perfectly good airfield. There may be sufficient height in hand to manoeuvre for a normal, but close, circuit; or otherwise a crosswind, rather than a difficult downwind, contra-traffic landing.

On the other hand there will be a minimum 'decision height' below which a turn-back for a landing in any direction could clearly not be accomplished; and of course there will be an associated maximum distance. The only logical basis for opting for a turn-back, rather than landing somewhere within that 120° arc ahead of you, is a properly derived decision that it is by far the safest choice. This requires knowledge of the dynamics involved in the turn-back and of the relevant characteristics of the aircraft being flown. Knowledge of the latter can only be gained by practising accurate, low-speed, fully banked gliding turns at a safe height and measuring the height lost in the turn plus the distance:height ratio at Vbg.

6.3 Turning back — procedure and dynamics

The repositioning manoeuvre
210 degree turn-backTurning back to land on, or parallel to, the departure runway is a two-stage procedure. This comprises a repositioning manoeuvre, turning through maybe 210°, so that the aircraft is positioned as close as possible to the extended runway line at sufficient height to then glide directly back to the planned touchdown point at Vbg — the speed that provides the best L/D ratio and thus optimum distance in a straight glide. A small turn will be needed to finally align with the selected landing path.

If the take-off has a crosswind component, the initial turn should be conducted into the crosswind so that the aircraft will drift towards the extended runway line and also reduce the ground diameter of the turn a little. If the take-off has been downwind because of runway slope then the minimum height for a turn-back would be greatly increased; if there are any doubts don't turn back — except as needed for an into-wind off-field landing.

Of course there is no need to opt just for a runway if you have departed from a larger airfield with ample cleared area available for an emergency landing.

While repositioning, it is important to minimise the time spent in the turn and thus the height loss, so gliding at Vbg or even Vmp is not a requirement; but choice of an optimum turn speed is vital.

Turn speed, diameter and rate of turn
The air radius of a turn is directly proportional to the true airspeed squared and indirectly proportional to the angle of bank. The rate of turn is directly proportional to the angle of bank and indirectly proportional to the speed. Table 5.1 shows some calculations for various bank angles at speeds of 40, 50, 60 and 70 knots. The calculations are based on two slightly simplified but accurate equations applicable to all light aircraft:
  • The turn diameter (metres) = the airspeed (metres per second) squared divided by 5 × the tangent of the bank angle.
    Example: airspeed 60 knots (30 m/sec), bank angle 30° and tangent 30° is close to 0.6.
    Turn diameter = 30 × 30/5 × 0.6 = 900/3 = 300 metres.

  • The rate of turn (degrees per second) = the tangent of the bank angle × 1100 divided by the airspeed in knots.
    Example: bank angle 45°, tangent 45° is 1.0 and airspeed 40 knots.
    Rate of turn = 1.0 × 1100/40 = 1100/40 =28°/sec.
    So time to turn through 210° = 8 seconds.

  • Note 1: a rate 1 turn is 3°/sec, a rate 2 turn is 6°/sec, a rate 3 turn is 9°/sec, and a rate 4 turn is 12°/sec. Very heavy transport aircraft normally turn at 1.5°/sec.

Table 5.1 Turn diameters and turn times
(knots CAS)
TangentTurn diameter
Turn rate
Time to turn
through 210°
40 10° 0.2 400 m 5 42 s
(20 m/s) 20° 0.4 200 m 11 19 s
  30° 0.6 135 m 16 13 s
  45° 1.0 80 m 28 8 s
  60° 1.7 45 m 48 4 s
50 10° 0.2 625 m 4 53 s
(25 m/s) 20° 0.4 310 m 9 23 s
  30° 0.6 210 m 13 16 s
  45° 1.0 125 m 22 10 s
  60° 1.7 73 m 38 6 s
60 10° 0.2 900 m 3.7 57 s
(30 m/s) 20° 0.4 450 m 7.4 28 s
  30° 0.6 300 m 11 19 s
  45° 1.0 180 m 18 12 s
  60° 1.7 105 m 32 7 s
70 10° 0.2 1225 m 3.1 67 s
(35 m/s) 20° 0.4 610 m 6.3 33 s
  30° 0.6 410 m 9 23 s
  45° 1.0 245 m 16 13 s
  60° 1.7 140 m 27 8 s

It can be seen that both a greatly reduced turn diameter and a very fast turn rate are achieved at the lowest speed coupled with the highest bank angle, with the bank angle being more significant than the airspeed. So the stall speed of the aircraft has some importance; the ultralight with a very low Vs1 can produce a very fast small diameter turn. Note from the table that at all speeds the time to turn through 210° and the air diameter of the turn are around four times better with 60° bank than with 20°. However, the third factor to be considered when selecting the bank angle and airspeed is the rate of sink relative to the bank angle.
Bank angle, stall speed in the turn and rate of sink
The 'turn forces' diagram shows the relationships between total lift force, bank angle, weight and the centripetal force required to make the turn.

 Turn forces diagram

In the turn, the vertical component [Lvc] of the total lift force just about balances aircraft weight, and the horizontal component of lift [Lhc] provides the centripetal force to minimise the turn radius. At 30° bank angle Lhc = 0.6 Lvc while at 60° Lhc = 1.7 Lvc. So to provide the centripetal force for a sustained turn, the wing loading must be increased by pulling g as angle of bank increases; rather slowly up to a bank angle of 30° — where it is 15% greater than normal level flight loading — after which it escalates.

The diagram is for a powered level turn, but the principles are much the same for a gliding turn. Except that in the level turn, the airspeed is generally held constant and the increase in total lift force is gained by increasing angle of attack; the consequent increase in induced drag is countered by increasing thrust. In a gliding turn the increase in total lift force is obtained by both increasing the angle of attack (pulling g) as bank increases and increasing the airspeed by lowering the nose; the rate of sink accelerates as airspeed and aoa (thus induced drag) increase.

Table 5.2 is a sample profile of the increase in sink rate in a sustained gliding turn at particular bank angles. The base sink rate is the minimum sink achievable in a straight glide at Vmp. The fourth column shows the increase in turn stall speed and the last column is a representative estimate of the increase in rate of sink in the turn if the airspeed chosen was about 10% higher than the turn stall speed [i.e. for 45° bank airspeed = 1.3 Vs1]. Note: L/D or glide ratio [actually Lvc/D] deteriorates markedly as bank angle increases because of the escalating induced drag as more g is pulled.

Table 5.2: stall speed/sink rate in a sustained gliding turn
Bank angleCosineLoad factor
(=1/cos angle)
Vs1 multiplier
Sink rate multiplier
(See note 1 below)
10° 0.98 1.02g 1.01 (+1%) 1.05 (+5%)
20° 0.94 1.06g 1.03 (+3%) 1.15 (+15%)
30° 0.87 1.15g 1.07 (+7%) 1.3 (+30%)
45° 0.71 1.41g 1.19 (+19%) 1.9 (+90%)
60° 0.50 2.00g 1.41 (+41%) 3.5 (+250%)

Note 2: the comparative sink rates shown in the right-hand column will vary substantially with each aircraft type/model. The late Tony Hayes of the Thruster Operations Support Group kindly produced some Thruster T300 trial data, which showed that in a 45° bank gliding turn at 55 knots (1.3 Vs1) the sink rate was 900 fpm, or 3 times the Vmp sink rate of 300 fpm. If the turn was conducted at 59 knots (1.4 Vs1) the sink rate increased to 1050 fpm or 3.5 times minimum sink in a straight glide. The sink rate in a straight glide at Vbg (48 knots) was 400 fpm.

The trials were conducted soon after sunrise in a calm, stable atmosphere thereby providing best results. Sink rates would be worse in normal everyday conditions.
Choosing the bank angle
Obviously the height lost in the turn is a function of the rate of sink and the time spent in the turn. Table 5.3 is a calculation for a hypothetical ultralight that has a Vs1 of 40 knots and a minimum rate of sink in a straight glide of 420 fpm or 7 feet per second. The airspeed selected for the turn is just 10% greater than the stall speed (Vs[turn]) at those bank angles.

Table 5.3 Height lost in a 210° turn.
(Vs1=40 knots, minimum sink =420 fpm or 7 fps)
Bank angleVs (turn) +10%
Turn diameter
Turn time
Sink rate
Height lost in turn
10° 44 540 m 46 7+ 330 ft
20° 45 280 m 24 8 190 ft
30° 47 190 m 15 9 135 ft
45° 52 135 m 10 13 130 ft
60° 62 110 m 7 24 170 ft

It can be seen that a 45° bank angle, where Lhc = Lvc — i.e. the wing loading is equally distributed between countering gravity and providing the centripetal force — allows the least height loss. The height loss at a 30° bank angle is much the same but the lesser bank gives a larger turn diameter. Bank angles less than 30° or greater than 45° are not as efficient in terms of height loss. Similar relationships are found for other light aircraft, so 45° is the usually accepted optimum bank angle for least height loss and smaller diameter. The POH may recommend otherwise if high-lift devices are fitted.

There is a problem with choosing and maintaining a particular bank angle, in that if the aircraft is not equipped for flight in instrument meteorological conditions there is no reliable instrumental means of accurately assessing the bank angle — though fortunately pilots tend to overestimate (rather than underestimate) the steepness of the bank by perhaps 10°, i.e. they believe they have 45° bank but in reality it is perhaps only 35°. The angle can only be confidently established by comparing the horizon with ascertained structural or cockpit angles.

6.4 Turning-back

A possible scenario
Imagine a competent aviator who has practised for steep turn-backs (at a safe height and maximum weight) and can hold the aircraft at constant speed with a constant bank angle known to be 45° and, by trial, has established the average rate of sink in such a turn. Vsi for the aircraft is 40 knots CAS and Vbg is 60 knots CAS. As a result, the pilot feels comfortable using an airspeed that is only 10% greater than the stall speed in a 45° banked turn — that speed is 52 knots and thus the average turn diameter is 135 metres, rate of turn is 21°/sec, and rate of sink is 900 fpm or 15 feet per second.

Suppose that pilot takes off towards the north on a 600-metre north-south strip sited in rough terrain; there is nil wind and smooth ISA sea level conditions. The aircraft lifts off 200 metres from the southern end, climbing away at 60 knots (30 m/sec) and 500 fpm. The engine fails 60 seconds after wheels-off when the aircraft is 500 feet above airstrip level and 1800 m from the lift-off point, or 1400 m from the northern threshold. The pilot takes 4 seconds to react to the engine failure (see 'Engine failure after take-off') and decides on a turn-back. A further 5 seconds passes before the aircraft is established in the glide at the speed appropriate for the turn, i.e. 52 knots. The slow speed roll rate is around 15–20°/sec, so another 2 seconds passes before the turn is established. Thus about 10 seconds elapses between engine failure and start of turn. During this time the aircraft moves about 250 m further from the airstrip and loses perhaps 50 feet of altitude, so at start of turn the aircraft is 450 feet above runway level and 1650 m from the northern threshold.

With a turn rate of 21°/sec and sink rate of 15 feet/sec, the 210° turn takes 10 seconds during which the aircraft loses 150 feet. So after straightening up and establishing descent at Vbg, the aircraft is 300 feet above strip level and a bit less than 1650 metres from the airstrip. So the elapsed time from engine failure to being in a position to start the straight line return glide is about 20 seconds, during which 200 feet of altitude is lost while the aircraft has moved nearly 250 m further from the runway.

Let's presume the aircraft's L/D is 10:1, so to glide 1650 metres after straightening up it would have to start from a height of 165 m or 540 feet. Starting from only 300 feet it will hit the ground about 750 m short of the runway, so in this scenario the distance to glide after the end of the turn is of more importance than height lost in the turn.

If the aircraft had taken off into a 10-knot (5 m/sec) headwind, then the end-of-turn point would be displaced 80 seconds × 5 m/sec = 400 m closer to the threshold, with then 1250 m to run. At the 60-knot Vbg and 70-knot (35 m/sec) ground speed descent the 1250 m would be covered in 36 seconds. The aircraft's L/D is 10:1 so the Vbg sink rate is 6 knots or 10 feet/second. Thus the aircraft will lose 360 feet during the glide indicating that, even with the favourable 10-knot wind, it will hit the terrain 200 m or so short of the threshold.

The aircraft might just scrape in for a successful turn-back in nil wind conditions if the initial climb rate was such that it is 750 feet agl at 60 seconds after wheels-off, in which case it would be at 550 feet at end-of-turn.
Choosing a safe speed
Obviously you shouldn't conduct a low-level turn near the point of stall and any mishandling or turbulence during turns at high bank angles and low speeds may result in a stall-spin event, so a minimum safety factor for the turn must be considered. For a recreational light aircraft a factor of 10% above Vs[turn] may not be enough, so perhaps the turn speed should be 20% greater; i.e. 1.2 times Vs[turn]. For the example in the preceding scenario, that safer airspeed at the required 45° bank would then be 58 knots CAS — which might increase rate of sink from 15 to 17 feet/sec, the turn time from 10 to 11 seconds and thus the height loss in the turn from 150 to 190 feet; acceptable, considering the added safety.

However, the stall speed at 45° bank is 1.2 × Vs1 CAS and multiplying that by 1.2 provides an airspeed of 1.44 × Vs1 CAS — close to our normally recognised safe speed of 1.5 × Vs1. So then considering all the inaccuracies inherent in flight we come back to 1.5 × Vs1 CAS (60 knots in the scenario) as the optimum speed in the 45° banked turn-back manoeuvre.

Extract from an RA-Aus fatal accident report: 'Following the loss of power at approximately 300 feet, the pilot apparently attempted a turn to the left in an attempt to return to the runway that he had just departed from. At a position approximately 200 metres to the left of the extended centre line of runway 30 and 400 metres from the upwind threshold of that runway, the aircraft entered a spin and impacted the ground in a near vertical attitude.

Note 3: In the preceding tables and text I have used the calibrated airspeed but the velocity in the equations should be the true airspeed, so the turn diameter will be greater than shown, the rate of turn will be less and consequently the height lost during the turn will be greater.

6.5 So what's the verdict?

From the foregoing you might conclude that it would be foolish to state (though many do) that a return to the runway is possible if a particular aircraft type is above a certain height when EFATO occurs.

The main factors to be considered/estimated in the very few seconds available for an informed decision are these:
  1. The distance you are from the nearest runway/airstrip threshold and the distance you will be when the 45° bank re-positioning turn, flown at 1.5 × Vs1 CAS, is completed and the aircraft established at Vbg.
  2. The estimated height still in hand after the repositioning turn is completed and whether that will be sufficient for the glide approach to the threshold.
  3. The effect wind and turbulence will have on the result.
  4. Although EFATO operations are near ground level the effect density altitude will have on the result must be taken into account. For example, as TAS increases with density altitude then the height loss during the turn at a particular CAS must increase.
  5. The existence of obstructions along the glide path.
  6. Possible collision avoidance risks in the contra-traffic landing — emergency, low-level, non-powered manoeuvring may lead to a stall/spin event.
  7. If very close to the airfield, can sufficient height be lost to land reasonably safely, taking wind effect into account.

All of this indicates that the possibility of success is very difficult to assess quickly when airborne time remaining is rapidly counting down to zero. You must know your aircraft and your capabilities, and have previously established the safe turn-back performance under varying conditions. Also you must be a very good judge of distance (few pilots are) and be able to maintain absolute control at rather low energy levels and higher wing loadings; otherwise — it is most unwise to turn back!

The next article in this series discusses the sometimes dangerous effects of wind shear and turbulence events.

'Decreasing your exposure to risk' articles

| Introduction and contents | Recent RA-Aus accident history | Don't fly real fast | Don't stall and spin in from a turn |

| Don't land too fast in an emergency | Engine failure after take-off | The turn back: possible or impossible — or just unwise? |

| Wind shear and turbulence |

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