Most pure angle-of-attack indicators are not really very useful for performance monitoring or even stall warning without additional filtering or damping inputs, since the indications fluctuate so quickly, and are so sensitive to control inputs. The LRI does measure a differential pressure that is directly proportional to angle-of-attack, but it is also directly proportional to dynamic pressure (q in engineering terms).

 

[In the discussions below, (x) represents multiplied by.]

 

Mr. Morgan Huntington claimed that the fundamental mathematical expression of the LRI was expressed:

 

 

DP = q (sinF - sinB)

where,

DP = differential pressure

q = free stream dynamic pressure = 0.5(x) rho (x) V squared

when,

rho = air density

V = velocity

 

and the angular terms are as laid out in the patent description, or shown in figure 1 of the Embry-Riddle report.

 

Although this mathematical expression has not been clearly documented, and is probably not exactly correct, we can conclude that DP is directly proportional to q and also directly proportional to angle-of-attack. This represents one of the unique advantages of the LRI, since these two quantities are the only two parts of the lift equation that a pilot can change (for a given aircraft). More specifically,

 

L = 0.5 (x) rho (x)V squared (x) S (x) CL = q (x) S (x) CL

where,

L = total lift

q = dynamic pressure

S = wing area

CL = lift coefficient (proportional to angle-of-attack)

 

To simplify things a bit, the pilot can control both angle-of-attack, within the limits of elevator authority, and q, within limits of engine power output (within a range of speeds further defined by drag rise due to wing stall on the low end, and top speed limited by aircraft form drag). By measuring an aerodynamic quantity proportional to both q and angle-of-attack, we have a better measure of total lift than an angle-of-attack meter could ever provide.

MAXIMUM LIFT PERFORMANCE

 

Total lift produced is not just a function of angle-of-attack, but also dynamic pressure:

 

1/2 rho (x) velocity squared

 

At 10 knots on the takeoff roll, you can put a wing at any angle-of-attack you want, but without more speed you still have zero total lift. Conversely, you can have 300 knots of airspeed, but without positive angle-of attack on a symmetrical airfoil, you still have zero total lift. (Note: you can think of cambered airfoils as having some "angle-of-attack" pre-built into them). The LRI measures both essential quantities. 

 

The LRI is calibrated to a fixed reference point that is very useful for attempting to maximize aircraft performance, or if expressed from a safety viewpoint, to safely operate the aircraft throughout the flight envelope.

 

The fixed reference point might be evidenced differently depending on the particular flying qualities of each aircraft type. For example, it might be evidenced by:

 

  1. aerodynamic stall in unaccelerated level flight
  2.  

  3. adverse accelerated stall characteristics in maneuvering flight,
  4.  

  5. in an aircraft with a less well-defined "stall" (or even "stall-proof" aircraft such as an Ercoupe), it might be defined by aft stick travel limits for landing in ground effect at forward cg
  6.  

  7. in an aircraft without a strong stall "break" (such as a Stinson 108, or most light Cessnas at forward cg, it would be manifested by "mushing" flight or unacceptable rate-of-sink. 

 

This fixed reference point seems to have been alternately referenced as stall, point of zero lift reserve, onset of mushing flight, etc. (The FAA term in vogue seems to be minimum controllable airspeed.) The point is, that for a given aircraft, that reference point, once determined, can be referenced again and again regardless of changes in air density, temperature, density altitude, vertical acceleration (g-load or load factor), wind and gusts, and (at least for light aircraft) changes in aircraft gross weight.

 

Once this point is established, other points in the flight envelope can be easily defined through some simple flight tests, since we know:

 

STALL SPEED: the LRI reference point, as discussed above.

 

BEST GLIDE: most distance covered over the ground for a given altitude loss, occurs at L/D max, easily referenced to the LRI.

 

BEST RANGE: maximum distance flown for a given fuel state, also occurs at L/D max.

For single-engine fixed gear aircraft, occurs at approximately: 1.6 (x)Vs1.

Single-engine retractables: 2.0 (x)Vs1.

Light twins: 1.7 (x)Vs1where, Vs1=clean power-off stall speed.

 

BEST ENDURANCE: maximum time aloft for given fuel remaining.

For single-engine fixed gear aircraft, occurs at approximately 1.2 (x) Vs1.

For single-engine retractables or light twins, 1.3 (x) Vs1.

 

MINIMUM SINK RATE: gives the most time aloft for a given loss of altitude, and corresponds to the same point in the flight envelope as best endurance.

 

BEST ANGLE OF CLIMB: gives the greatest altitude gain for the horizontal distance covered, for takeoff obstruction clearance.

 

BEST RATE OF CLIMB: greatest altitude gain in a given time span.

 

SHORTEST TAKEOFF ROLL and SHORTEST LANDING ROLL: both directly proportional to margin above stall.

 

ETC, etc.

 

The LRI is a much more useful tool than just being a stall warning device. It gives a repeatable indication of all these performance maxima and minima independent of all the variables given above. Thus we can safely and confidently operate the aircraft across a much broader range of the flight envelope.

 

Most of the values listed in the manuals of current production aircraft are somewhat conservative. Manufacturers are very liability conscious, especially in the low-speed regime. But there are some variations in performance from aircraft to aircraft, even off the same production line, and even more variation in static source position error from one airplane to the next. So some of the "padding" accounts for those differences. But older aircraft, produced before about the mid -1970s or so, are probably "padded" in the other direction, claiming performance that the production aircraft could never quite live up to. So the flight manual is a good starting point for the determination of the performance capabilities of each aircraft, but there is likely much to be gained by running an abbreviated flight test program for each aircraft as they calibrate their LRI. It certainly builds the owners confidence and proficiency as well.

 

Sometimes it is hard to bridge the gap in understanding between engineers and pilots. Engineers may find this discussion lacking in academic rigor, but at least it is a starting point in understanding what the LRI can do for us operationally.