... probably because there are very few definite, right answers to many of these sorts of questions ...
1. Clearway.
Increased clearway generally is of use if
(a) it doesn't extend beyond the limiting TOD/TOR considerations .. i.e. there is a limit to the amount of clearway (included in TODA) able to be used before the TORR becomes limiting or, if you prefer, there is a limit to the proportion of the airborne flare distance to 35 ft which can be over the clearway. This limitation is to give you some confidence that you will be off the ground before you run out of hard surface. As a result, a very lengthy declared clearway often is only partly usable for a particular aircraft.
(b) any resulting increase in RTOW (or MTOW if you prefer) doesn't push the net flight path further out sufficiently to cause conflict with terrain which it missed at a lower weight
(c) on another tack, if RTOW is not a pressing problem, you may be able to use some more clearway, subject to (a), to permit a reduction in V1 and provide some (more) ASD stopping margin.
If the aim is to maximise RTOW, then one would normally push the V1 up to achieve (or approach) an ASD limited takeoff. This minimises the V1 to VR acceleration distance so that the clearway can best be used to get a bit more RTOW. Definitely a case of juggling the numbers to get the best compromise result .. as the particular case which provides the lowest takeoff weight becomes the limit for the particular conditions there is no point in pushing one limit weight up if another goes down in consequence.
If the aim is to get some extra ASD margin, then one would reduce the V1 until either TORR or TODR becomes limiting.
Generally, there would be not much point in keeping V1 the same as the previous value has already given a limit case for one of the various calculations .. with the same V1, the takeoff doesn't vary unless the TODR was the significantly limiting case. In this situation, you might get an improvement in RTOW at the same V1 as there would be some ASD, TOR, and (with the additional clearway) TOD available with which to play.
I think Empty Cruise is assuming a limiting ASDR and has overlooked TORR ?
2. Slats and flaps.
Slats and LE flaps tend to extend the basic wing CL vs alpha curve to higher alpha and CL. Trailing edge flaps tend to shift the basic curve to a higher CL range. With both on board, the effect is cumulative. The answer to your question is, I suggest, probably not answered simply as one has to think about, in addition to the body angle, the flight path angle, the changed airflow patterns due to the devices, and where the wing sees the wind coming from as a result (alpha) .. a fairly dynamic situation. I shall be interested to see what answers other people might come up with during the life of this thread.
3. Density height simplified calculations.
A reasonably accurate calculation is -
DH = PH +/- (120 * ISA deviation in deg C)
As the equations are straightforward to program into a spreadsheet once the constants are put in, you might like to play with them on your PC. For the troposphere, the basics are
(a) temperature in Kelvin (K) = 273.15 + OAT (C)
(b) ISA temperature (K) = 288.15 - 0.0019812 * height (ft)
(c) temperature ratio = theta = OAT (K)/288.15
(d) pressure ratio = delta = theta^5.25588
(e) density ratio = sigma = theta^4.25588
Using the non-dimensional quantities, theta, delta and sigma makes the sums easier and, for the latter two, we avoid having to work with dreadful numbers
(f) having picked a height, calculate the standard temperature, theta, delta, and sigma. These are the figures you will find in ISA tables. If you wanted to know the actual pressure and density values, you could multiply the non-dimensional values by the sea level values ... not much point in that, though.
(g) to allow for a non-standard temperature, the general relationship is
sigma = delta/theta
(h) so calculate theta for the non-standard condition (c) and then sigma (g). Delta is standard as we are considering the situation on 1013 mb with a non-standard temperature only. As has been suggested earlier, if the QNH is not 1013 then a correction needs to be made to bring us back to standard pressure conditions.
(i) then go back to the standard atmosphere equation for sigma (e) and figure a standard height which has the same sigma as calculated in (h). This calculated standard height is referred to as the density height .. ie the height in ISA where the actual density (or density ratio) is located.
Having always just used 120 ft/deg as the correction, which I read somewhere when I was learning to fly, I thought it would be fun to do the above and check it out. Looking at a few heights from sea level up to 15000 ft and deviations from ISA of up to +/- 30 C, (and assuming I haven't made any careless mistakes), the correction rates vary non-linearly but within a small band ranging between about 110 and 130 ft/deg. Looking at a straight line curve fit for constant heights, the average correction is around 119 ft/deg, so call it 120 ft/deg to make the mental arithmetic reasonable... any error is not so great as to have any operational significance.
Last edited by john_tullamarine; 15th Apr 2002 at 02:59.