# What does the term "Course Cut Limit" mean in relation to an autopilot?

In several manuals detailing the autoflight systems of some aircraft, it is common to see the VOR/LOC capture mode have something called a 'course cut limit.' What is this term referring to? I am writing the code for a 747 autopilot based on the gain values given by NASA, and the VOR mode description includes the line "A 34 degree course cut limit is provided."

I have tried googling for this answer but all I could find was some vague definitions saying that this is a guidance control parameter limiting the intercept angle of a capture mode.

So in my example, does this mean that the autopilot will turn my 747 to intercept at no more than a 34 degree angle? If so, at what point does this turn occur? Is it when the capture submode engages? It can't be before that, as before that the autopilot is still referenced to the heading bug while waiting for an intercept/capture.

Thanks! Chris

• Is this a sim autopilot? Jan 1 at 8:57
• Yes, this is a sim autopilot. Jan 3 at 4:26

This document holds more information on the topic, the document states on page 4:

A course cut limit L was applied to the cross-track bank-angle input when the airplane was a long distance from the horizontal path

Furthermore a diagram is given on page 16 figure 6, which nicely visualizes this:

The functioning is described as:

When the airplane has a cross-track error greater than $$3\cdot r_t$$, the airplane flies toward the path so that $$\phi_I = 90^\circ$$ The angle $$\phi_I$$ decreases linearly from $$90^\circ$$ to $$30^\circ$$ as the cross-track error decreases from $$3\cdot r_t$$ to $$1.5\cdot r_t$$.

Thus the "Course Cut Limit" simply limits the authority of the crosstrack limit to the bank angle.

I programmed something similar some while ago, and actually came up with an remarkably similar solution, however only 40 years later :D.

• Thank you! I feel as though I am very close to understanding. So in the case of my 747 autopilot, the VOR capture logic works off of beam error and course error. The course cut limit of 34 degrees is applied to the beam error according to my block diagram. I am confused as to how the beam error and course cut limit work together in this instance. Capture begins once beam error is less than 5.8 * sin (course error). Dec 11, 2022 at 0:33
• @ChristopherHelton note that the $e_{ct}$ is the crosstrack error, this is the perpendicular distance to the desired path. The course cut limiter is however dynamically scheduled as seen in the document I linked. I am a bit confused however why $\phi_I$ is held constant at $30^\circ$. I do not see how an assymptotic capture is made possible with this limiter... Dec 11, 2022 at 19:56
• It seems that the course cut limiter on my 747 autopilot is not dynamically scheduled in any way. I understand that beam error in degrees is essentially equivalent to a crosstrack distance, but no further specification on how the course cut limit works is provided in my documents. I tried an implementation where the beam error signal is not applied until course error is less than the course cut limit of 34 degrees, but this just caused the autopilot to make a strong turn to capture the course, before turning back the other way into an asymptotic capture. Dec 13, 2022 at 8:43
• The beam error is not equivalent to crosstrack distance, but rather to the derivative of the $e_{ct}$. Hence the gains $K_y$ (for the crosstrack) and $K_\dot{y}$ for the beam error. This structure represents a PD controller for the crosstrack distance! This is also why you get such nice assymptotical capturing properties. I would just limit the upper output of $e_{ct}$ and forget about the lower limit. Perhaps you can disable the beam error path when the upper limit is active. That should work. Dec 13, 2022 at 10:33

I'm not a software programmer but have flown functional test flights on newly installed autopilot systems. If you replace the word "cut" with "capture" that makes sense to me. With the Collins systems I operated, I would tune the localizer, engage Heading mode and set a heading using the heading bug to intercept the localizer course, arm the Approach mode, and as the localizer guidance indicator came alive ("off the peg") the Approach mode would activate (capture) the localizer and the Heading mode would disengage. The difference between my heading and the localizer course was limited prior to capture otherwise the aircraft (traveling up to 250 Knots) would pass right through the localizer centerline and require too great a turn radius to successfully execute the approach (bank angles were limited with the autopilot engaged and further dampened or "smoothed" during localizer approach capture mode). a difference of 34 degrees sounds about right for the maximum.

After some digging, I came across a swell piece of information in a Qantas 747 maintenance training course about the autopilot, describing the INS capture function:

"When crosstrack distance is greater than 1.5nm, the crosstrack error signal is given a simulated error of 1.5nm until actual crosstrack distance is less than 1.5nm. Combined with a track angle error signal, this limit gives a 25° intercept angle until crosstrack distance is less than 1.5nm, at which point fine capture begins."

In essence, the crosstrack error is limited to 1.5nm, or approximately 9000 feet. The error on the autopilot for crosstrack error in the INS mode is 8.85° bank angle command per 1000 ft of crosstrack distance error. Track angle error is summed into this command at a gain of 3.16° bank per degree of track error. Combined together, this gives an approximately 25° intercept angle when CTD is at the limit of 9000 ft/1.5nm.

After realizing this, everything else clicked.

In the VOR mode, where course cut limit is 34 degrees, beam error is limited to about 4.63 degrees (though capture can begin at a larger beam error of up to 5.8 degrees) so that, combined with course error, the intercept angle is approximately 34 degrees until actual beam error is less than 4.63, at which time full capturing begins.

Likewise, in the LOC mode where the course cut limit is 25°, the beam error is limited to 1.67° (again, capture and intercept happens sooner), so that intercept happens at a 25° angle until actual beam error is less than 1.67°.

Implementation in the sim like this works perfectly. Thanks for your help and input everyone!