ROC 3 ROC 4
Stick & Rudder
IN OCTOBER'S "TF.ST PILOT" you learned how to fly a climb performance flight
Determine the height of
The technique of flying a series of climb flights at
Performance Data Reduction
d i f f e r e n t airspeeds a n d recording c l i m b data
Turning flight-test data into something usable
through several altitude blocks was straightforward, but we cautioned you
test u s i n g a modified c h e c k - c l i m b procedure.
about the sensitivity of the data to the way you fly the tests. We stressed
precise airspeed control, repeatability, test-planning judgment, and the importance of your qualitative remarks, all of which have a say in the accuracy of your data and the usefulness of your test results. Now that you have all your data cards brimming with numbers, it's time to transform them into somet h i n g useful. The data reduction process is a little time-consuming but not difficult. This month our goal is to determine which airspeed yields the best climb rate, what that climb rate is, and how VY and climb rate vary with density altitude.
This month our goal is to determine which airspeed yields the best climb rate, what that climb rate is, and how VY and climb rate vary with density altitude. for your flight-test and postflight data reduction numbers. Figure 1 repeats that grid with test data numbers that came from a single test flight, i.e., a single climb airspeed. You should
have a set of data like these for every Crunching Numbers
Last month we provided a data grid 102
airspeed tested. Let's see how to get the Calculated numbers.
each altitude block by subtracting the bottom of the
block altitude (PAD from the top of the block altitude (PA2). Calculate the rate of
climb (ROC) through each block by dividing the block height (Diff on the grid) by the t i m e it took to c l i m b through it (see formula be-
low). If the block is in feet and the time is in seconds, multiply the result by 60 to have the answer in feet per minute. ROC =
PAZ - P41 x60 Time
Altitude blocks were necessary for timing, but they're cumbersome to use for flight planning. It's easier to use the block's midpoint altitude. This is consistent with using the average ROC through the block, but we know that the airplane climbs marginally faster at the bottom and marginally slower at the top of the block. Your postflight data check for reasonableness should have assured no significant ROC: change within the altitude blocks, and this assurance lets us use the midpoint of the blocks. The midpoint of each a l t i t u d e
Start Weight 1260 lb
PA1 PA2 Diff Mid OAT DA
Time ROC FPA
25 40 55 75
9500 h_J>- 9250
tude block, and the OAT column contains the outside air temperature (in degrees Celsius for our example) for the middle of the altitude blocks. Using a density altitude chart or flight computer, determine the density altitude (DA) for each altitude block midpoint and enter these on the grid. Put this data grid aside and repeat the n u m b e r c r u n c h i n g for every tested airspeed. When you're finished, you should have several grids, each pertaining to a specific test airspeed.
End Weight I240lb
1500 1200 750 550 400 : 1
It's time to draw, and you'll need some graph paper. Starting with one grid, i.e., one airspeed, plot ROC vs. DA as shown in Figure 2a and fair a line through the data points. This line shows your climb rate for any density altitude between the mid-
Bottom of pr«i«ut« altitude block
Altitude block height Midpoint ot altitude block
RA2 Top of prtnurc attitude Mock OAT
Outtide air t«mp
True airspeed Elapsed time through block
Rate of climb Flight path angle
block is simply the altitude halfway
them in the Mid column on the grid. The Mid column contains pressure altitudes for the middle of the alti-
between PA 1 and PA2. Calculate the midpoints for each block and enter
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point of the lowest a l t i t u d e block and the midpoint of the highest altitude block for one airspeed.
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Density Altitude Figure 2a
VI > V2 > V3 > V4
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Density Altitude Figure 2b
Repeat this plotting exercise for every airspeed you tested. When you're done, you should have a plot that resembles Figure 2b. (To minimize clutter, the example has only four tested airspeeds.) The more airspeeds you test, the better your climb performance accuracy will be. We labeled our example tested airspeeds from fastest to slowest as VI through V4, respectively. Figure 2b indicates airspeed V3 yields the fastest climb rates of the airspeeds tested, hut we don't know if there's some other speed that is slightly faster than V3 (between V2 and V3) or slightly slower than V3 (between V4 and V3) that produces an even better ROC. To find this intermediate speed, you'll create a new plot of ROC vs. Airspeed from your existing ROC vs. DA plot. In Figure 2b draw a vertical line up from the DA axis through the lines of different airspeeds. Draw horizontal lines from the ROC axis to the intersections of the vertical line you just drew and each airspeed line the vertical line passes through (Figure 3a). Now you can read the ROC for each corresponding airspeed at this density altitude. Create a new plot (Figure 3b) of ROC vs. Airspeed, by plotting the corresponding values from Figure 3a, and fairing a curve through these points. You can now see the maximum ROC occurs at the top of the curve at a speed
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Figure 3a ROC 3
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between V2 and V3. Because the vertical line in Figure 3a represents a single DA, the curve in Figure 3b applies only to that single DA. Repeat this cross-plot procedure for several density altitudes, i.e., several vertical lines on the ROC vs. DA plot (our example uses three). It doesn't matter which DAs you choose, hut it's a good idea to space them evenly. Your plot of ROC vs. Airspeed should now look like Figure 4a. The peaks of each curve represent the maximum ROC and V Y for each density altitude. To find the maximum climb rate for any of the plotted DAs, draw a horizontal line from the peak of the DA curve to the ROC axis. To find VY, draw a vertical line from the peak of the DA curve to the horizontal axis. Although Figure 4a provides a lot of very useful information, it's still a bit cumbersome. If you draw a line connecting the peaks of the DA curves, you can now find VY and its associated ROC between the plotted DAs. The problem is that you must interpolate between the plotted DAs. Another cross-plot will solve this. To create a plot of VY for all density altitudes, draw vertical lines from the peaks of the DA curves down to the Airspeed axis as shown
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in Figure 4b. Where the vertical lines cross the Airspeed axis is the VY for that DA. Use these V Y /DA data pairs to create a new plot of VY vs. DA (Figure 5a). Fair a line through the data points. The final step is just labeling another vertical axis on Figure 5a. The dashed line connecting the peaks of the curves in Figure 4a shows the relationship between V Y and ROC. Draw a series of vertical lines from the Airspeed axis up to this dashed line. Then draw horizontal lines from the ROC axis to the intersections of the dashed line and vertical lines you just drew. Notice that for every V Y there is only one ROC associated with it, regardless of density altitude. Draw another vertical axis on the right side of Figure 5a so it looks like Figure 5b and annotate the ROCs associated with the VYs directly across. Now you have a handy, singlesource plot t h a t shows your airplane's V Y and ROC for a range of density altitudes. No more looking up tables or percentage calculations for nonstandard temperatures or wondering about the applicability of the airplane manufacturer's claimed climb performance.
These data are useful for variations in climb schedules. Figure 4a, for example, shows the ROC penalty you'll pay if you choose to perform a cruise-climb at a speed faster than VY for better engine cooling or outside view over the nose. You can create a plot similar to Figure 5b by using your cruise-climb airspeeds instead of the peaks of the DA curves on Figure 4a. Sounds like a winter project, doesn't it? Yes, we went t h r o u g h a lot of number crunching, plotting, and cross-plotting this month, but we transformed all your raw climb performance data into a single plot for your operator's manual. Next time we'll f i l l in the V, and I;1'A columns on the data grid. We'll do a little more math and a lot less plotting as we complete our data reduction by explaining how to take that same raw data and determine your airplane's maximum climb angle and the airspeed at which it occurs (Vx). Until then, please keep sending your comments and questions to Test Pilot, EAA Publications, P.O. Box 3086, Oshkosh, WI 54903-3086 or edit[email protected]
>eaa.org with TEST PILOT as the subject of your e-mail.