In the following we'll show an interactive demonstration about anticipating / leading the (standard rate) turn when passing a fix, and I will show a few tables I have computed that show the lead distance (early turn distance) and optimal bank angle. It's called "leading the turn", and the FAA also uses the term "early turn".
If you start your (standard rate) turn at the specified distance from the fix ("marker"), you are correctly anticipating/leading the turn, and don't overfly the fix first, which would require you to re-intercept the outbound radial behind the fix, which would result in a ground track similar to that of a snake-trail, before you can join the outbound radial. The FAA asks us to anticipate/lead our turns, but gives no guidance as to how to do that, i. e. WHEN (or WHERE) to start the turn. See the more detailed discussion below.
The following interactive graphic shows what is going on: drag the sliders for your TAS and the turn angle, and observe the distance by which to pre-empt/anticipate the turn in red, as well as the optimal bank angle, also in red. Again, this was computed for standard-rate turns. When you fly this maneuver in the cockpit or simulator, the only numbers you need to manage are beginning the turn at the "marker" (fix minus distance, red segment) and the optimum bank angle. Both are shown in red. You don't need to care about the turn radius, I have shown it only for illustrative purposes (so you can see how it increases as TAS increases).
The FAA asks us to anticipate/lead our turns, but gives no guidance as to how to do that, i. e. WHEN (or WHERE) to start the turn. The IFH doesn't mention this topic at all, and the IPH mentions it twice without providing any further guidance. The AIM says the following in 5-3-5:
5-3-5. Airway or Route Course Changes
a. Pilots of aircraft are required to adhere to airways or routes being flown. Special attention must be given to this requirement during course changes. (...)
An early turn, as illustrated below, is one method of adhering to airways or routes. The use of any available cockpit instrumentation, such as Distance Measuring Equipment, may be used by the pilot to lead the turn when making course changes. This is consistent with the intent of 14 CFR Section 91.181, which requires pilots to operate along the centerline of an airway and along the direct course between navigational aids or fixes.
b. Turns which begin at or after fix passage may exceed airway or route boundaries. FIG 5-3-1 contains an example flight track depicting this, together with an example of an early turn.
c. Without such actions as leading a turn, aircraft
operating in excess of 290 knots true air speed (TAS)
can exceed the normal airway or route boundaries
depending on the amount of course change required,
wind direction and velocity, the character of the turn
fix (DME, overhead navigation aid, or intersection),
and the pilot's technique in making a course change.
For example, a flight operating at 17,000 feet MSL
with a TAS of 400 knots, a 25 degree bank, and a
course change of more than 40 degrees would exceed
the width of the airway or route; i.e., 4 nautical miles
each side of centerline. However, in the airspace
below 18,000 feet MSL, operations in excess of
290 knots TAS are not prevalent and the provision of
additional IFR separation in all course change
situations for the occasional aircraft making a turn in
excess of 290 knots TAS creates an unacceptable
waste of airspace and imposes a penalty upon the
preponderance of traffic which operate at low speeds.
Consequently, the FAA expects pilots to lead turns
and take other actions they consider necessary during
course changes to adhere as closely as possible to the
airways or route being flown.
The AIM mentions the following in the context of RNAV waypoints (section 1-2-1 b. 1):
(a) Fly-by waypoints.
Fly-by waypoints are used when an aircraft should begin a turn to the next course prior to reaching the waypoint separating the two route segments. This is known as turn anticipation.
(b) Fly-over waypoints.
Fly-over waypoints are used when the aircraft must fly over the point prior to starting a turn.
Another reason to avoid overflying a VOR or intersection directly is the fact that oftentimes more than one airway meet/join over a VOR or intersection, causing traffic to converge over these fixes. The AIM tells us in 4-4-15 e.:
e. Traffic at VOR Sites. All operators should emphasize the need for sustained vigilance in the vicinity of VORs and airway intersections due to the convergence of traffic.
It means that if we don't even fly over the fix in the first place, we do our (small) contribution to lower traffic convergence over the fix. Also keep in mind, VFR traffic uses VORs and airways as well. They may not talk to ATC, and ATC may miss a traffic alert, so we should do our own part in terms of collision avoidance and not just rely on ATC. Leading our turns is one such (small) part as we'll miss the fix completely, by at least several hundred feet, or more.
Here is a table showing you the distance (in nm) from the fix at which you should start your standard-rate turn, and the associated optimal bank angle (in degrees), to join the outbound radial after the fix again. The following assumes that you do the turn with standard rate, i. e. 3 degrees per second. This is important to note. But, it is recommended practice for IFR flying anyway to always use standard rate, unless you have reason not to. For cruise flight on airways, we don't really have a lot of reasons to justify not using standard rate turns (although half standard rate also has its advantages, see below). You could also use your autopilot, many autopilots either use standard rate by default for their simple turns, or allow you to set that you want to command the turn with standard rate. And, of course, when I programmed the math, the table, and the interactive graphic above, I assumed zero-wind conditions. Needless to say, this is only valid when the winds are calm, as there is no wind correction / crab angle included in the computations.
Locate your KTAS in the top row (yellow background) and your turn angle in the left column, and then you find your optimal bank angle in the second row (yellow background), and your distance from fix to begin your standard-rate turn in the table. For example, if your TAS is 180 ktas and your turn angle is 120 degrees, your optimum standard rate bank angle is 26 degrees, and you should start your turn 0.55 nm (horizontal distance taken from the GPS) from the fix.
Here is a download link that shows a scenario I have flown with Microsoft Flight Simulator X and recorded as a clip. With 109 KIAS and a pressure altitude of 5,000 ft. and a temperature of 4C (resulting in 117 KTAS) and using a 90 degree turn, we look up a bank angle of 18 degrees and a lead distance of 0.64 nm. In the video clip, we fly on the 090 degree radial towards the VOR, and at 0.64 nm we turn N with standard rate. The second VOR shows us the 360 degree radial as a reference, and we see that we level out on a heading of 360 on the 358 degree radial (we missed it by one dot, or 2 degrees).
Download Link
Here is a table using half standard rate turns, i. e. 1.5 degrees per second, instead of 3 degrees per second. The distances are twice the distances of the standard rate table above (as turn radius is proportional to speed), but the bank angles are not (as they are related to speed through the inverse tangent).
Here is a table for higher speeds, such as used by airliners, using half standard rate turns as well, i. e. 1.5 degrees per second.
We don't show a table for standard rate turns for airliners, as the bank angles would be too steep -- as per FAA recommendation, all bank angles in IMC should be limited to 25 - 30 degrees, and airliners adhere to that. 380 KTAS require 46 degrees of bank, 600 KTAS require 65 degrees of bank. At these bank angles we'd also get load factor / G force problems. As you'll remember from flight school, at 45 degrees bank angle load factor increases by
41% (sqrt(2)), and at 60 degrees bank load factor doubles (1/cos(60 deg), it means you'd be twice as heavy as you are, with the corresponding additional stress and wear on the plane). At 70.5 degrees bank angle load factor actually TRIPLES!
Note the following:
As you approach the fix on the blue straight segment, begin your bank for standard rate (second row from table above) when you reach the red segment. This is the distance shown in the table above.
You end up flying along the blue curved segment (blue arc segment on the circle).
The distance is horizontal distance from the fix, NOT slant distance. So you should be using your GPS or FMS to determine your "marker distance", NOT your DME. This is also more consistent, because if the fix is not a VOR/DME or VORTAC but an intersection or NDB or simple VOR (without DME or TACAN), you would practically have to use your GPS or FMS anyway to find its distance from you. I generally assume everyone has at least a hand-held VFR GPS on board, for exactly these simple purposes: find (non-slant) horizontal distance from any fix.
Turn Angles less than 90 degrees (acute angles) are unrealistic, we don't find them on airways. We have merely shown them for illustrative purposes and for practice. (You are encouraged to practise the above turn anticipations / early turns a few times in VMC or in the simulator before flying them in actual IMC.)
A slight error is introduced by the fact that when you start a turn, you are not immediately banking with your target bank angle. The plane takes 1 - 2 seconds (or possibly more) to reach the target bank angle you determine. In fact, you SHOULD give the plane its time, because an abrupt jerking of the yoke means undue stress on the plane, which can cause breakage, and at least excessive wear. So, despite the computations I have made for you, please continue to be gentle to your plane when entering and leaving the turn!
Note that we are using KTAS here, not KIAS or KCAS. Thus, if you are at altitude (which is where you SHOULD be cruising), make sure you don't just look up your KIAS from the airspeed indicator in the first row of the table. You have to use your KTAS (compute it with your E6B, "1.6% per 1000 ft. of alt" rule-of-thumb, or GPS/FMS/G1000). This is because from basic physics and math, we need to use Newton's free body motion law, which uses actual velocity in space, and that is KTAS and nothing else.
You will probably remember from flight school the rule-of-thumb you were taught for the bank angle for a standard-rate turn: drop the last digit of your airspeed, and add 6. This is equivalent to dividing your airspeed by 10, rounding down to the next integer, and adding 6. Some instructors teach it as simply dividing by ten, not rounding down. Others round to the next multiple of 10 and then drop the last digit (aka: divide by ten). Another rule-of-thumb divides the speed by 10, and then adds 50% of that value. This table compares the four methods against the exact bank angle (blue):
This looks reasonably close for the speed range that most GA planes cruise at: 90 through 180 ktas. In particular, the rule of thumb "divide by ten, and then add half of that value" comes VERY close to the exact formula (compare blue and orange). Here we show an error/difference plot, showing the differences (errors) of the approximation formulas to the exact formula:
For most pilots it's hard to keep the bank angle constant within +/- 1 or 2 degrees anyway, but the error/difference plot shows even better how good the "divide by ten, and then add half of that value" formula is (orange). However, the tables above are exact. You may want to print them out and make them part of your kneeboard.
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Copyright (c) 2012 Andreas Lauschke Consulting. All Rights Reserved.