Process for preventing undesired contact with land or water by low-flying aircraft
The invention relates to a process for preventing undesired contact with land or water by low-flying aircraft, such as are prescribed a minimum altitude and are provided with measurement devices for altitude, rate of descent (or airspeed and path angle). 
     An alarm for detecting inadmissible rates of descent of an aircraft is known from German Offenlegungsschrift No. 2,139,075, when nearing the ground as a function of the height above the ground and of its time-derivative, the alarm comprising an altimeter measuring the height above ground and a differentiating component generating a rate-of-descent signal proportional to the derivative of the height above ground, and a limiting device restricting the amplitude of the rate-of-descent signal provided to avoid false alarms. The altitude of flight h T  at which the alarm is triggered is determined from the equation: 
     
         h.sub.T = -h.sub.T ·T.sub.D + h.sub.T.sup.2 /2ng 
    
     where 
     h T  is the rate-of-descent when the alarm is triggered (h T  = h) 
     T D  is the pilot&#39;s reaction time, plus a safety factor, 
     n is a constant and g is gravity acceleration. 
     Since this alarm is lacking automatic actuation on the path control loop, it cannot be applied to unmanned aircraft. 
     The present invention addresses the problem of creating a process for preventing unwanted contact with land or water by low-flying aircraft when the minimum flight altitude depends upon the instantaneous flight parameters and on the possible subsequent path resulting therefrom. 
     Various process modes are provided to solve this problem in the manner of the invention. In all processes, a boundary or limiting altitude depending upon the maximum admissible transverse acceleration will be continuously determined from measurements of rate-of-descent (or from airspeed and path angle) and from the instantaneous transverse acceleration (with elimination of gravitational acceleration), the aircraft not being allowed to descend below the limiting altitude. If it descends lower, there will be a non-linear actuation on the path control loop in such manner that the aircraft path will be corrected at the maximum admissible transverse acceleration. 
     In one process, the invention calls for the limiting altitude to be tabulated as a function of the instantaneous transverse acceleration, of the airspeed, and of the path angle (or of the rate of descent), and to be stored in a computer, the data being provided from simulation or from test flights. 
     In another process, the invention determines the limiting altitude by the formula ##EQU1## b QB  is a reference acceleration (positive) which as a rule will be selected equal to the maximum transverse acceleration; b Q  is the instantaneous transverse acceleration; T bQ  is a time constant from the dynamics of the acceleration control loop of the aircraft; H is the rate of descent and ΔH min  is a predetermined minimum altitude. The term H 2  /b QB  then corresponds to the expression h 2   T  /(2ng) of German Offenlegungsschrift No. 2,139,075. The expression ##EQU2## is modified with respect to -n . T D  of the Offenlegungsschrift. The fraction ##EQU3## takes into account that during the transition period until the maximum transverse acceleration, the influence of the acceleration in the desired direction will be the more prevalent the closer the value of b Q  at the onset of the correction process was to -b Qmax . Further, the origin of factor T bQ  is different from that of T D . 
     Another process of the invention applies to measurement methods in which the altitude is erroneous because determined normally to the longitudinal axis of the aircraft, as in laser beam methods. Denoting the erroneous measurement values for H and H (resp.) by H M  and H M , the formulas for the limiting altitudes become 
    
    
     Further advantages, characteristics and applications of the invention will be further illustrated in the accompanying drawings, in which: 
     FIG. 1 is a sketch for determining the kinematic height; 
     FIG. 2 shows the individual parameters of the limiting-altitude; 
     FIG. 3 is a control loop for dynamic path-limiting; 
     FIGS. 4 through 7 are artist&#39;s renditions of the limiting trajectories; 
     FIGS. 8 and 9 show the impulse-response to transverse acceleration for a system of minimum phase and for one of a no minimum-phase (b Qc  is the reference to transverse acceleration); 
     FIG. 10 elucidates some measurement variables; and 
     FIG. 11 is a sketch illustrating the measurement of altitude and of rate of descent by means of lasers. 
    
    
     The process of the invention is applied to prevent unwanted contact by aircraft with land or water. When applied over land, the assumption is flat terrain or small hills. This process also may be advantageously applied to maintain the altitude of aircraft, very swift change to new reference altitudes being especially feasible. Application thereof extends both to manned and unmanned aircraft. 
     Measuring instruments for the parameters below are located aboard an aircraft 2: 
     for altitude H, 
     
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speed v,                                                                  
                     (or rate of descent H. )                             
angle of path γ,                                                    
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     and instantaneous transverse accleration b Q . 
     If with elimination of gravitational acceleration the aircraft moves in an arc of a circle at constant acceleration b Q , then the loss in altitude will be given by ##EQU5## 
     The aircraft 2 in the position shown subtends an angle of path-γ with respect to a horizontal reference line 4&#39;. If aircraft 2 when flying along the arc of a circle 6, shown in dashed lines, comes to position 2; then its angle of path γ will be zero. Reference line 4 represents the ground surface, or that of water. FIG. 1 clearly shows that the limiting altitude H limit  always must be larger than ΔH kin  in order that contact with the ground be reliably avoided. 
     However, since topographical idiosyncracies must be accounted for, or the state of the water, the aircraft is predetermined to be at a minimum altitude ΔH min  which is to be heeded at all times for safety reasons. 
     If the aircraft 2 at the beginning of the time under consideration has not yet acquired the transverse acceleration b Q  = -b Qmax , then the limiting altitude H limit  must be increased by a certain amount ΔH dyn , as shown in FIG. 2, because of the delay which occurs between the reference transverse acceleration b QC  = (-b Qmax ) and the actual transverse acceleration b Q  (determined by the inertia of the aircraft), so that one will always have 
     
         H ≧ H.sub.limit = ΔH.sub.kin + ΔH.sub.dyn + ΔH.sub.min 
    
     There will be continuous determination of H limit  during flight and comparison with the actual altitude H. 
     For H ≧ H limit , the control 8 of the aircraft will remain unactuated, but for H &lt; H limit , a drive transverse acceleration will be imparted to the aircraft, the acceleration being b QC  = -b Qmax . 
     FIG. 3 shows a control loop 10 for dynamic path limiting. The values H, v, b Q  and γ (or H, H and b Q ) are measured inside the aircraft 2 and supplied to the computer 12 calculating H - H limit . If the results show that the difference is larger or equal to zero, then the control 8 will remain inactive. If the difference is less than zero, then maximum transverse acceleration -b Qmax  will be commanded. The regulator 14 for the transverse acceleration control loop may operate linearly or nonlinearly and will not be further described here. 
     Magnitude ΔH min  is predetermined in order to fix H limit , and ΔH kin  may be determined from ##EQU6## The term ΔH dyn  determined by the dynamics can be obtained precisely only by continuous pre-computation. This requires solving a differential equation describing the relationship between the commanded reference transverse acceleration b QC  and the future actual transverse acceleration b Q . Further, one must obtain the relationship between b Q  and the resulting rate of descent H (&lt;0), from which one must obtain ##EQU7## where τ is the integration variable, T dyn  the time interval until the commanded reference transverse acceleration b QC  becomes -b Qmax  within a given tolerance band of 5% of b QC . If before reaching b Q  = -b Qmax  the aircraft passes through the path minimum, then ΔH kin  drops out and ΔH dyn  becomes correspondingly smaller. 
     The continuous pre-computation of ΔH dyn  can be accomplished only at high computer cost. The designs described below as embodiments of the process on the other hand may be achieved at low computer cost. 
     In one embodiment of the process, the limiting flight paths of the aircraft are obtained by off-line simulation or by actual flight tests, as follows: 
     1. At the beginning of the computation (t=t o ) of each path a through g, let the angle of path always be γ(t o ) = γ o  = 0, let the initial speed v o  = v(t o ) and the actual transverse acceleration b Qo  = b Q (t.sbsb.o.sub.) ≧ 0 be parametrically predetermined. 
     2. first let b Qo  vary for fixed initial speed from b Qo  = 0 to b Qo  = b Qmax , there being switching on of 
     
         b.sub.QC = -b.sub.Qmax 
    
     when t A  = t o  (FIG. 4). 
     3. then the switch-on time t A  + t o  + τ -- with τ≧0 -- will be varied for γ o  = 0 and b Qo  = b Qmax , τ max  being determined by γ o  ≧γ&gt; -90° (FIG. 5). 
     4. The paths will be so computed until γ = 0 again (path minimum) and thereupon all paths (a through g) will be so shifted that their path minima coincide (FIG. 6). 
     5. The same process subsequently will be carried out for various initial speeds v o . 
     Each point within the shaded &#34;region of danger&#34; in FIG. 6 is uniquely determined by the values H limit , v, b Q  and γ, as shown by the lines γ = constant and b Q  = constant (FIG. 7), so that the measurement of v, b Q  and γ, (and hence) 
     
         H.sub.limit = H.sub.limit (v, b.sub.Q, γ) 
    
     may be uniquely determined. The points (H limit , v, b Q , γ) as a rule being discrete, H limit  will be determined by interpolation or by postulating the particular most unfavorable boundary values for v, b Q  and γ. 
     In actual design, a table with input values of v, b Q  and γ and of the associated resulting value H limit  will be stored in the computer memory. The corresponding analog representation is qualitatively shown in FIG. 7. The latter illustrates the case of the aircraft at time t = t being in the mode b Q  (t) = b Q1 , γ (t) = γ 2 , v and H(t). 
     FIG. 7 shows a graph with γ= constant and b Q  = constant, and allows obtaining H limit  (t) and the horizontal distance x M  - x FG  to the path minimum. In the example shown, H&gt;H limit , that is, the path control loop will not be activated. If the aircraft maintains the value of b Q , its path will be increasingly steeper, whereby the drawn-in point along the b Q  = b Q1  wanders upwardly until H = H limit . Because of the ensuing activation (of the control loop) the aircraft will move along a limit trajectory (H = H limit ) as far as the path minimum, where the control loop again will switch over to normal operation. 
     This process may be simplified because the limit trajectories are determined only for the most unfavorable value of speed v, that is, for that value of v (within the admissible range) entailing the least maneuverability of the aircraft. In lieu of v and γ, one may introduce H as a parameter, so that now 
     
         H.sub.limit = H.sub.limit (H, b.sub.Q). 
    
     the limit altitude so obtained however will always be larger than in the preceding version of the process, so that activation of path control will occur prematurely. 
     In another mode of the process, the dynamic component of the limit altitude, ΔH dyn , is obtained as an estimate. This includes the system response to an impulse function from the commanded transverse acceleration from b QC  = +b Qmax  to - b Qmax , where b Q  = b QC  = b Qmax  prior to the impulse. The time T bQ  denotes the interval to reaching for the first time the value b Q  = -b Qmax  (see FIGS. 8 and 9). FIG. 8 shows the acceleration for a minimum-phase system (canard type planes) and FIG. 9 shows the acceleration for a non-minimum phase system (tail-engine driven aircraft). 
     Given that 
     
         H = v sin γ, 
    
     the dynamic component of limit altitude approximately is obtained from ##EQU8## where, if a larger value of T bQ  is inserted, allowance can be made for a safety factor. The limit altitude H limit  then will be given by 
     
         H.sub.limit = ΔH.sub.kin + ΔH.sub.dyn + ΔH.sub.min. 
    
     Measurement of altitude and of rate of descent may be effected by radio means or by barometric altimeters. 
     FIG. 10 provides the relationship 
     
         θ = α + γ 
    
     where θ is the angle of position of the aircraft with respect to a geodesic reference line and α the angle of attack of the aircraft 2. The altitude H and rate of change in altitude H for barometric altimetry may be carried out independently of the angle of position θ within certain limits (approx. ± 30°). 
     Using suitable estimates and approximation formulas, one may then obtain ##EQU9## without having to know γ, α or θ. 
     
         H = v · sin γ ##EQU10## whence ##EQU11## for H≦0. 
    
     H limit  will be used in the control loop of FIG. 3. 
     In a further embodiment of the process, the measuring instrument will sense H and H normal to the longitudinal axis of the aircraft, for instance by laser methods (FIG. 11). If θ ≠ 0°, this will cause spurious effects, because then ##EQU12## hence ##EQU13## In particular 
     
         Δ H.sub.dyn = -H · T.sub.bQ, H ≦ 0, ##EQU14## and ##EQU15## 
    
     The magnitude of Δ H min  for H→0 or H limit  will be of maximum weight because in that case H dyn  →0 and also H kin  →0. In order not to introduce spurious effects in Δ H min  for horizontal flight, the expression Δ H min  /cos θ is therefore replaced by Δ H min  and therefore I bQ  is increased by a sufficient amount so that within the range of values for H that is of interest, the actual limiting altitude will always be less than the computed one. One obtains therefore the formula: ##EQU16## 
     It will be obvious to those skilled in the art that many modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications.