Effective Date: 15 June 98
INTRODUCTION
In response to the questions of acceleration-stop distance and the definition and diagram of the tracks of takeoff, inflight and approach, the following information is submitted. The questions cannot be simply answered as both the ground portion of the problem both taking off and stopping and the inflight portion, are interrelated, since one depends upon the other. Because of this, the discussion will cover takeoff speed determination, takeoff distance determination, accelerate-stop determination and flight profile determination. The airfield problem is divided into three sections to enhance your understanding of the various details of the effort. They are: Segmentation, Analysis and Procedures.
The total effort is an iterative process in that you must obtain many small segments of the supportive data, allow time to analytically combine these pieces of data and then demonstrate that the data generated is valid in the view of the certifying agency. In general, within the civil certification testing, the applicant usually has to perform the test program to gather data to present to the agency to show that the airplane will meet all of the certification criteria and then repeat critical portions of the certification demonstration with the agency on board to both monitor and actually flying the test airplane.
Takeoff Speed Analysis
Figure 1 will be discussed several times in this report. This figure is complex as it presents all of the interrelations of accelerate, stop, controllability, and climb including the FAR factors. For this reason, the report will spend more time on this figure now to give the reader an overview of the most complex performance problem of all; the critical field length.
Overview
The chart development begins with minimum unstick speed, VMU and continues through the go-takeoff into the takeoff safety speed, V2. This is done for each ambient temperature, pressure altitude, wind and gross weight desired for certification. This part of the mathematics develops the decision speed for either Go or NO-GO called V1. It is at this point the calculations turn to the stopping portion of the problem. In the math, the reader methodically selects a progression of engine failure speeds, each of which meet the requirements such that it must be greater than Ground Minimum Control Speed, VMcg. The problem then continues with the calculations to a single rotation speed for both the All-Engines-Operating (A-E-O) and the One-Engine-Inoperative 0-E-I condition. This single rotation speed is developed from the Vmu A-E-0 and O-E-I factored up by 1.08 and 1.05 respectively and then incremented back to rotation speed by the delta-speed from the normal rate rotation to lift-off for each of the two conditions. Maximum rotation rated demonstration data is used here, then the higher of the two rotation speeds is selected.
Next the delta-speed from lift-off to the 35 foot obstacle height is computed. If this produces a Takeoff Safety Speed, V2 that is less than the V2 min, then the selected V2 has to be increased to accommodate the minimum requirement. The lift-off speed and the rotation speed must also be increased accordingly. Similarily, the minimum V2 must meet the minimum climb gradient.
At this point, the stop portion of the problem is considered. As the V1 was selected for this one case, time delays tied to the reaction the pilot demonstrated plus one second for each action he must make is computed and the speed where braking, thrust decay and such is initiated, is computed. Maximum brake energy demonstrated must not be exceeded. The All-Engine-Operating distance using the All-Engine- Operating speeds is also computed and then increased by 15%. Once the distance calculations are performed using these three criteria, the longer distance of the three is used for one point on the flight manual chart .
Development
Here begins the chart development part of the discussion. (It should be noted that the order of the presentation is not necessarily the order that the tests were performed.)
VMU
The Minimum Unstick speed for both All-Engines-Operating and One-Engine- Inoperative are summarized on a single plot such as Figure 2. The thrust to weight ratio, T/W existing at some reference speed reflecting engine cut is used.
Also note here that the VMU speed is divided by the stall speed for the particular run as with all of the data presentations. This is for convenience as most of the FAR factors are presented as percentages.
dVROT max
Next the incremental speed between rotation and lift-off at the maximum practical rotation rate is presented. Figure 3 shows that T/W at lift- off is used as a basis.
VLOF min
Figure 4 shows where the chart array is constructed for a range of T/W's. One chart for A-E-O and one for O-E-I begin with VMU which are factored up by 1.05 and 1.08 respectively to product the minimum lift- off level. Then the VLOF min is reduced using the incremental rotation- to-lift-off speed increment gathered from the maximum rotation rate tests. Here, two rotation speeds exist.
VROT max
As shown on Figure 5 the rotation speeds are combined, factoring T/W by the number ratio of O-E-I to A-E-O to be able to put both rotation speeds on the same scale. For example, for a four engine airplane this factor is 3/4; for a three engine airplane, this factor is 2/3.
Now the highest rotation speed of the two is selected for the single rotation speed chart.
V35 Obstacle Speed
Figure 6 presents the data gathered from the normal rate A-E-O and O-E-I tests as shown here are added to the single rotation speed value to produce the chart for the speed at the 35 foot [V35] point.
Figure 7 is an example of a condition where the V2 speed at 35 foot does not achieve 1.2V2.
Backing down from 1.2VS by the V35 - VR increment shows the initial VR was higher than that obtained. So, as illustrated on Figure 8, the VR has to be adjusted up on the lower (left) side of the chart to make sure that 1.2VS (at a minimum) is obtained at the 35 foot point.
Using this technique, as shown on Figure 9, one can produce the rotation, lift off and safety speed charts for use in creating the takeoff distance calculations.
Then, by referring back to Figure 1 the unique interrelation of these values should now be a little clearer.
Review
Briefly, the chart development begins with minimum unstick speed, VMU. The single rotation speed is developed from VMU. A-E-O and O-E-I factored up by 1.08 and 1.05 and incremented back to rotation speed by the delta-speed from rotation to lift-off for each of the two conditions. The maximum rotation rated demonstration data is used here and the higher of the two rotation speeds is selected. Next, the delta- speed from normal rotation rate lift-off to the 35 foot obstacle is computed. This produces a takeoff safety speed, V2 which may have to be increased to accommodate the minimum requirement. The lift-off speed and the rotation speed must also be increased accordingly. Remember that minimum V2 must meet the minimum climb gradient.
Stopping Speeds
Once again, referring to Figure 1, you can see where the transition is made to the stop portion of the problem again beginning with the selected accelerate-go engine failure speed. It shows that beginning with the previously selected engine failure speed, VEF, the V1 selected for this one case includes the time delays tied to the recognition the pilot demonstrated following engine cut.
Correlation Factors
As with analysis of most of these segments, the conditions existing during the test run are input to the equation and any distance error would be ratioed. This term is called a K-factor and this K- factor would then be correlated against the most likely influence such as gross weight. In general, the K-factor should approach the value of 1.0.
Segmentation Relations
Figure 10, Figure 11and Figure 12 are presented to illustrate the extent of segmentation necessary for the airfield analysis.
Based upon the segmentation illustrated in Figure 10, Figure 11and Figure 12 , a generalization in equations can be developed which can be used for,
Methodology
These segmetations share a common theory and in turn a common derived equation format which is illustrated as follows. From this illustration, using Figure 13 to sum the forces along the acceleraton path yields,Equation 1
AEO Correlation
The AEO acceleration segments correlation is generally computed by assiging the K-factor on the total "right hand side" of the equation. (Other analysis approaches might have placed the K-factor on the term or group that are least known. ) The AEO correlation presented here uses the overall correlation procedure. After a lot of mathematics, this generalized correleation equation for the All-Engine-Operating (aeo) acceleration segment becomes ,Equation 2.
The resulting correlation is generally presented as shown in Figure 14.
Now, Figure 15shows that, beginning with the previously selected engine failure speed, Vef and up to the beginning of another segment such as rotation, the "V" selected for this case inherently includes the actual time delays tied to the recognition the pilot demonstrated following engine cut and thrust decay of the segment.
Rotation Correlation
The rotation distance correlation is done for both the AEO and the OEI rotation increments up to lift off. The segment is defined by th e initiation of rotation to the lift off point. Data for specific test runs are input into the fiollowing basic equation inEquation 3 and Kr() is produced.
The K-factors generally correlate Figure 16; one for AEO and one for OEI.
Braking Coeffiecient
Equation 4presents the braking expansion equation. Prior to this expansion, the reduction of the test data must be done.
As shown on Figure 17 , instead of solving for a K-factor, the previous equation is rearranged to solve for the braking coeffficient, Mu-b. Here, the typical Mu-b presentation versus the ground speed Vg. The flat portion indicates the brake torque limit area and the sloping portion the maximum rubber to concrete capability. If brake fade occurs, the sloping line will be reduced at the higher energy levels.
Here, inEquation 5 , the action segment equations reflect the pilot demonstrated times plus one second for each action he must make is computed and the speed where braking, thrust decay and such is initiated, is computed. Maximum braking energy demonstrated must not be exceeded. In the braking segment of the problem, this relation is used for the flight manual expansion.
The correlation of the thrust decay segment using Equation 6 is conventional with the exception that the transitional average thrust, T-avg must be input into the equation.
Not all test runs need to be performed with an engine fuel cut. This is acceptable provided that adequate accountability of the transient differences between throttle chop to idle and fuel cut can be demonstrated as illustrated on Figure 18. The utilization of the throttle chop to idle aids flight safety in cast of the real loss of another engine. The idled engine can then be advanced to maximum if such occurred. It should be noted that hard engine fuel cuts do have to be demonstrated and as such, adequate overruns or emergency landing sites should be considered.
Alternate Correlation
An alternate method might be to correlate inclusive thrust decay time as indicated here on Figure 15, Figure 16 and Figure 18 for the Fuel Cutoff only. This, however, would presume hard fuel cuts as the ONLY demonstration technique.
The idle thrust segment would be the condition where all of the transients have been completed and the steady state problem occurs. Technically speaking, in Figure 17 (Fuel Cutoff), the muB term is the correlation constant for the segment, but a K-factor term is also computed to just show the deviation from 1.0 that would be obtained if the faired muB curve previously shown was used.
Flight Manual
Again, in the overview chart of Figure 1, you should now be able to see in more detail how the interrelation of stopping portion of the problem relates to the takeoff portion. Based upon the problem beginning with the selected accelerate-go engine failure speed, the stop portion of the problem begins. As the V1 was selected, time delays tied to the reaction the pilot demonstrated plus one second for each action he must make is computed and the speed where braking, thrust decay and such is limited and computed. Again, maximum brake energy demonstrated must not be exceeded.
This section basically presents the calculations for the flight manual distance for each point. Figure 10, the A-E-O segmentation case is illustrated. The calculations use the A-E-O speed developed earlier. For clarity, the A-E-O and O-E-I nomenclature is shown for a four engine airplane.
Keeping mind that the A-E-O distance using the A-E-O speeds is computed and then increased by 15% for comparison to the two other cases. Figure 11, the accelerate-go and Figure 12, the accelerate-stop calculations are performed also using the O-E-I speeds developed earlier.
Figure 13 presents the generalized forces produced during each of the ground segments and what this translates into for the computation of the segment distances. A typical A-E-O acceleration segment equation is shown, in Figure 14, along with the typical correlation factor presentation. Here, the Ka term was elected to be applied to the Cd minus muCl term as this is considered as an unknown variable. Alternately, it may have been elected to correlate only against the total measured distance and that computed with the equation with the Ka term as a multiple of calculated distance and not against the Cd - muC1 term as discussed above.
On Figure 12 is a possible engine transient segment calculation where the Ka term had been applied to the thrust to weight ratio existing just prior to engine cut and correlated to the delta velocity from cut to the end of the transient. This method does allow for variations between throttle chop and hard fuel cut.
On Figure 15 and 16, both A-E-O and the O-E-I rotation segments are shown along with the correlation term of each. Similar correlation as discussed for the transient section is also indicated. Again, on these figures, variations in correlation procedures may be elected by the contractors. Keep in mind that if the correlation statistical band is not adequate, the government agency may require the contractor to use the upper level of the band and thereby produce longer than average distances.
Still on Figures 15 and 16, the alternate method noted earlier had been used, these rotation and transient segment correlation and equations might look like this. Again, experience and computerized analysis aids greatly in isolating the optimum correlation of these terms.
The equation for climb-out segment and the forces encountered was initially developed from the energy equations and converted to the format noted here on Figure . The denominator of the equation is actually the climb gradient term.
Referring toFigure 26 , the climb-out correlation at the 35 foot point could typically be as shown and the distance calculated as such. If an alternate method was elected, the relation might be as shown.
Finally, on Figure 27, data correlation for the height of the gear up for use in flight manual chart development would be presented as such.
And now the last look at the overview chart of Figure 1. For the single ambient and gross weight condition and assumed engine failure speed, we have calculated the
o Engine-failure continued takeoff,
o the accelerate-stop run
o the all-engine-operating takeoff multiplied by 1.15.
Now the longest distance of these three is selected for the flight manual critical field length point on the chart candidate.
The next effort in the computing sequence would be to increase the assumed engine failure speed one knot higher and repeat the full expansion calculation procedure. This iteration loop will eventually provide the optimum CFL for this one ambient condition.
The ideal arrangement would be what is conventionally called the "balanced field length". This is where the accelerate-stop distance is equal to the accelerate-go distance and the All-Engine-Takeoff is less than both. Depending on the basic airplane design, such as under- powered engines and high braking capability, the balanced condition may not be atainable. However, the minimum distance can still be determined.
Takeoff Flight Path
Next, the takeoff flight path profile is best illustrated in the Figure 19 chart. This chart, which was extracted from FAR material, indicates the configuration of the various equipments on the airplane in the various segments.
The next figure, Figure 20 is also from FAR material and illustrates the basic requirements the airplane operator must follow. In planning the takeoff from any airfield within the certified environmeent, the operator may not load the airplane to a weight where the computed flight path does not clear all obstacles by 35 feet vertically or by at least 200 feet horizontally within the airport boundaries or 300 feet outside the airport boundaries. The manufacturer must provide material that allows the operator to compute the takeoff flight path for his specific conditions and confirm the airplane will meet the required clearance in all cases.
Typically, you provide four sets of charts; one for each segment. The distances obtained are added together and compared to the airport supplied obstacle profile. Generally the takeoff flight path continues to 1,500 feet although you must supply the enroute climb charts for long range obstacles. The first part comes from the CFL data which is the distance from brake release to the 35 foot point. The next partis to compute the climb-out profile for the many ambient combinations taking into account the landing gear retraction and effect on the profile. This chart reflects the typical "first segment" with gear down and "second segment" with gear up climbing to a minimum of 400 feet before accelerating while retracting takeoff flaps. The operator must assure there are no obstacles higher than the acceleration altitude before leveling and retracting flaps. Some airplanes may have to present a variable minimum flap retraction so that the All-Engine-Operating flight path is never less than the One-Engine-Inoperative flight path.
A typical acceleration distance to enroute climb speed is computed. Again, the acceleration altitude may be higher than the 400 foot level if an obstacle exists in the flight path. The final segment is with One-Engine-Inoperative and the flaps retracted at the final segment climb speed and is generally presented in the form of net climb gradient that can be used to compute far-out clearances. The typical net enroute climb gradient chart that must be produced to support the operating rules.
The data discussed thus far is used to develop the takeoff profile for the FAR Part 36 noise certification. The rules for developing the profile is discussed in the FAR in depth. The equations and database used in combination with the these rules will define the profile.