Aircraft Drag, Split from Flight Test and Limits Options

[dMz]

[EDIT: These 2 posts were split from "Flight Test and Limits" thread:
http://pilotsfor911truth.org/forum//index.php?showtopic=9433]

This is probably getting awfully "pilot speak" for some, but I've put together 2 new charts related to "Boeing" atmospheric drag calculations.

The first is an air density ratio vs. altitude chart. The "ratio" is the air density at various altitudes divided by the standard Mean Sea Level (MSL) air density (at 59 degrees F, or 15C, or 288.15 Kelvin). This is based upon data from Table IV of the US Standard Atmosphere 1976, compiled by NOAA, NASA, and USAF. Because I used the density ratio, the "ratio number" given by the chart should be able to be multiplied by whatever "standard" air density one prefers.

This Air Density chart is at:
http://www.orbitfiles.com/download/id3103238807.html

The other chart is a "Drag Ratio" chart for various "Boeing" flight envelopes based upon the NASA Glenn Research Center Drag Equation.

http://www.grc.nasa.gov/WWW/K-12/airplane/drageq.html

I "normalized" (or scaled) the chart for the smallest drag ratio I found (for a B757 at V_mo of 350 kts at 17,000 feet AMSL). I calculated the drag from velocities in 3 different unit systems and obtained the same drag ratios. I needed to make 2 assumptions in these calculations:

Assumption 1. The reference area "A_ref" will not change noticeably for a single aircraft at various altitudes.

Assumption 2. The complex Drag Coefficients (C_d) are not known at this time, and are not likely to be provided by Boeing any time soon. As the B757 is now an "obsolete" aircraft no longer manufactured by Boeing, my personal opinion is that this "proprietary" information has been withheld unnecessarily in the B757 case for 6 years. While the C_d values are probably very similar for B757-200 and B767-200 which are very similar aircraft, these values are unknown. If C_d values are obtained later, my Drag Ratio chart could be easily modified for better accuracy. The C_d values were assumed to be constant across all flight regimes (although I suspect that wind tunnel data should show different "C_d" cases for different air densities and speed ranges).

Based on the 2 assumptions above, I found the Drag [force] / (C_d * A_ref) quantities to compare the effect of relative velocity and various air densities on Drag [force] ratio. This requires the C_d and A_ref values to be reasonably constant and non-zero to be valid.

My "Drag Ratio" chart is at:
http://www.orbitfiles.com/download/id3103240377.html

The cyan bars are for the B757 family, since it has a slightly lower V_mo at 350 knots. The purple bars are for M_mo "mach" velocites, with M_86 being 0.86 mach M_mo for various altitudes, and the purple striped bars M_92 being the 0.92 mach "overtest" velocity referenced above on this thread. The green/red "V_OCT1K" bar is the 586 [statute] mph velocity that has been referenced in various places (NIST, MIT, FEMA/ASCE, etc.). The last 2 red bars represent the 0.86 and 0.92 mach velocities at 1000 feet AMSL for comparison.

Any "K" reference involves altitude (either 1K = 1000 feet AMSL, 17K, 25K, 35K = 35000 feet AMSL accordingly).

The "normalized" scale factor allows several unit choices- the preferred "standard" air density units at Mean Sea Level and 59 degrees F [ or 15C] multiplied by ONE of either [ 36088 kts^2, 47791 mph^2, OR 9551 m^2/sec^2 ]. If given the reference area "A_ref" and valid drag coefficient "C_d" for B757-200 or B767-200, then a close approximation to drag force should be obtainable from this comparative "Drag Ratio" chart. I found an increase of only +5.8% over the B757 V_mo at 17000 feet for the B767 at the slightly higher 360 kts V_mo, also at 17000 feet AMSL.

My notes from above: the alleged "586 mph" UA175 impact velocity is closer to the 0.86 mach drag level than it is to the 420 KCAS V_d "emergency dive velocity" drag level all at 1000 feet AMSL. The alleged "586 mph" drag level at 1000 feet AMSL is also ~3.297 times the B767 drag level at MAXIMUM V_mo of 360 knots at 17000 feet AMSL. It is also higher relative drag level than 0.92 mach "overtest" velocities at FL 250 and 350...

Engine thrust and survivability are FINITE resources, especially at higher air densities.

[amazed!]

dMole

Thanks for all that effort! (IMG:http://pilotsfor911truth.org/forum/style_emoticons/default/thumbsup.gif)

[dMz]

OK, let's start out with the more "basic" information here in light of recent discussion. From Anderson and Eberhardt's Understanding Flight:
------
"Drag
...Power is the rate at which work is done. In mathematical terms it is
also a force times a velocity. Drag is a force and is simply equal to
power/speed. We already know the dependence of induced and
parasitic powers on speed. By dividing power by speed, we have the
dependence of drag on speed. Since induced power varies as 1/speed,
induced drag varies as 1/speed squared. Parasitic power varies as
speed cubed, so parasitic drag varies as speed squared. Figure 2.16*
shows the dependence of induced, parasitic, and total drag on the
speed of the airplane

In the section preceding this one we saw that the induced
power increases as load squared. Since drag is just power
divided by speed, induced drag also increases as load squared.
Anything understood about power can be easily converted to
a similar understanding of drag by simply dividing by speed.
We have said that drag is part of a pilot’s culture and
vocabulary. That is true. But most of the time when the term
is used, the person really means power. Let us look at an
example to illustrate. Take the case of a pilot flying a small
plane with retractable landing gear. If full power is applied in
straight-and-level flight, the airplane accelerates to some speed and
goes no faster. A pilot might well say that the airplane’s speed is
limited by the drag.

Let us pretend that an airplane had two meters, one that measured
total drag and another that measured the total power for flight. We
will then record both values for the airplane at its top speed. The pilot
lowers the landing gear and flaps, leaving the engine at full power.
There is now a substantial increase in the drag and power required.
This of course slows the airplane down. We would find that the
airplane slowed down to the previous total power requirement and
now the total drag is higher than before. The pilot would have to
reduce power to bring the total drag down to its previous value. Its top
speed was not determined by the total drag but by the total power
(drag times speed). So, when pilots say drag they usually mean power.
The utility of the concept of power over drag for the pilot is fairly
easy to understand. Power requirements relate simply to the demands
on the engine. Drag is a force that must be related to the airplane’s
speed in order to understand the related power requirement to
overcome it. A drag of a certain value at one speed is only half the
power drain of a drag of the same value at twice the speed. In the end,
the power available from the engine is what counts.
------
* Although this isn't the exact drag vs. airspeed chart from the text, a similar one may be found at:

http://classicairshows.com/Education/Aerod...icsPartFour.htm

http://classicairshows.com/Education/Aerod...gVsAirspeed.gif
(IMG:http://classicairshows.com/Education/Aerodynamics/AeroDynamicsImages/TotalDragVsAirspeed.gif)

[dMz]

From Houghton and Carpenter's Aerodynamics for Engineering Students, 5th Edition:
-----------------
1.5.5 Types of drag
Attempts have been made to rationalize the definitions and terminology associated
with drag*. On the whole the new terms have not been widely adopted. Here we will use
the widely accepted traditional terms and indicate alternatives in parentheses.

Total drag
This is formally defined as the force corresponding to the rate of decrease in momentum
in the direction of the undisturbed external flow around the body, this decrease
being calculated between stations at infinite distances upstream and downstream of the
body. Thus it is the total force or drag in the direction of the undisturbed flow. It is also
the total force resisting the motion of the body through the surrounding fluid.
There are a number of separate contributions to total drag. As a first step it may be
divided into pressure drag and skin-friction drag.

Skin-friction drag (or surface-friction drag)
This is the drag that is generated by the resolved components of the traction due to the
shear stresses acting on the surface of the body. This traction is due directly to viscosity
and acts tangentially at all points on the surface of the body. At each point it has a
component aligned with but opposing the undisturbed flow (i.e. opposite to the direction
of flight). The total effect of these components, taken (i.e. integrated) over the whole
exposed surface of the body, is the skin-friction drag. It could not exist in an invisicid flow.

Pressure drag
This is the drag that is generated by the resolved components of the forces due to
pressure acting normal to the surface at all points. It may itself be considered as
consisting of several distinct contributions:
(i) Induced drag (sometimes known as vortex drag);
(ii) Wave drag; and
(iii) Form drag (sometimes known as boundary-layer pressure drag).

Induced drag (or vortex drag)
This is discussed in more detail in Sections 1.5.7 and 5.5. For now it may be noted
that induced drag depends on lift, does not depend directly on viscous effects, and
can be estimated by assuming inviscid flow.

Wave drag
This is the drag associated with the formation of shock waves in high-speed flight.
It is described in more detail in Chapter 6.

Form drag (or boundary-layer pressure drag)
This can be defined as the difference between the profile drag and the skin-friction
drag where the former is defined as the drag due to the losses in total pressure and
total temperature in the boundary layers. But these definitions are rather unhelpful
for giving a clear idea of the physical nature and mechanisms behind form drag, so a
simple explanation is attempted below.

The pressure distribution over a body in viscous flow differs from that in an ideal
inviscid flow (Fig. 1.13). If the flow is inviscid, it can be shown that the flow speed at
the trailing edge is zero, implying that the pressure coefficient is +l. But in a real flow
(see Fig. 1.13a) the body plus the boundary-layer displacement thickness has a finite
width at the trailing edge, so the flow speed does not fall to zero, and therefore the
pressure coefficient is less than +l. The variation of coefficient of pressure due to real
flow around an aerofoil is shown in Fig. 1.13b. This combines to generate a net
drag as follows. The relatively high pressures around the nose of the aerofoil tend to
push it backwards. Whereas the region of the suction pressures that follows, extending
up to the point of maximum thickness, act to generate a thrust pulling the aerofoil
forwards. The region of suction pressures downstream of the point of maximum
thickness generates a retarding force on the aerofoil, whereas the relatively high pressure
region around the trailing edge generates a thrust. In an inviscid flow, these
various contributions cancel out exactly and the net drag is zero. In a real viscous
flow this exact cancellation does not occur. The pressure distribution ahead of the
point of maximum thickness is little altered by real-flow effects. The drag generated
by the suction pressures downstream of the point of maximum thickness is slightly
reduced in a real flow. But this effect is greatly outweighed by a substantial reduction
in the thrust generated by the high-pressure region around the trailing edge. Thus the
exact cancellation of the pressure forces found in an inviscid flow is destroyed in a
real flow, resulting in an overall rearwards force. This force is the form drag.
It is emphasized again that both form and skin-friction drag depend on viscosity
for their existence and cannot exist in an inviscid flow.

Profile drag (or boundary-layer drag)
The profile drag is the sum of the skin-friction and form drags. See also the formal
definition given at the beginning of the previous item.
-------------------------------------------------
*For example, the Aeronautical Research Committee Current Paper No. 369 which was also published in
the Journal of the Royal Aeronautical Society, November 1958.

[dMz]

Perhaps there is a semantical difference in terminology in play here- let's see what the Wiki has to say:

http://en.wikipedia.org/wiki/Parasitic_drag

"Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. Parasitic drag is made up of many components, the most prominent being form drag. Skin friction and interference drag are also major components of parasitic drag.

In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing faster around protruding objects increasing friction or drag. At even higher transonic and supersonic speeds, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed."

http://upload.wikimedia.org/wikipedia/en/0...rag_Curve_2.jpg
(IMG:http://upload.wikimedia.org/wikipedia/en/0/04/Drag_Curve_2.jpg)

[rob balsamo]

... .and for extra credit, can anyone name the airspeed at which induced and parasitic drag cross? Hint: It was a very valuable number for Capt Sully... (IMG:http://pilotsfor911truth.org/forum/style_emoticons/default/wink.gif)

continuing...

Mcrit - also known as Critical Mach - is the airspeed at which airflow starts to become supersonic over a portion of a wing surface/body and is the critical airspeed at which total drag increases significantly until Mach 1.

Many who make excuses for the govt story regarding high speed flight always seem to forget (or intentionally omit) Mcrit and other types of drag which come into play.... wave drag being significant.

This is what happens to drag when an aircraft is traveling near its Mcrit speeds...

(IMG:http://www.aerospaceweb.org/question/aerodynamics/area-rule/transonic-drag.jpg)

As you can see, drag spikes/increases exponentially when passing Mcrit until Mach 1.

Sweep wing will "move" Mcrit closer to Mach 1, but as you can see, there is no escaping the effects of wave drag in transonic flight.

(IMG:http://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Wings/TH20G3.jpg)

This type of drag is how the Sound "Barrier" got its name and was a major problem when trying to break such a barrier decades ago.

Mcrit for a particular aircraft is usually very near Vmo/Mmo set by the manufacturer.

[Omega892R09]

... .and for extra credit, can anyone name the airspeed at which induced and parasitic drag cross? Hint: It was a very valuable number for Capt Sully... (IMG:http://pilotsfor911truth.org/forum/style_emoticons/default/wink.gif)

The airspeed was a value above the stalling speed one commonly known as minimum drag speed.

A question for thee. Which famous airliner routinely flew at below minimum drag speed during approach?

I find that Wiki definition of parasite drag, provided by dMole, rather odd.

Parasite drag is that drag other than the drag from lifting surfaces. This according to Kermode.

That drag coefficient / Mach No. graph is interesting (I was about to post on this and you beat me to it):
(IMG:http://www.aerospaceweb.org/question/aerodynamics/area-rule/transonic-drag.jpg)

The curve is often represented as a solid line with the exception of that hump between about Mach 0.82 and Mach 1.2 where a dotted line is used.

There is an interesting historical reason for this and yes it is linked to wave drag.

Anybody care to enlarge on that?

What many tend to forget is that although the aircraft's airspeed my be well below Mach 1 the velocity of the airflow over some parts may be transonic or supersonic.

It is the transonic region of flight which is the most problematic, until kinetic heating becomes a factor that is, and aircraft not designed for sustained flight at these speeds will tend to self destruct if such flight is attempted.

I believe I have raised the issue of critical Mach Number previously.

This post has been edited by Omega892R09: Apr 3 2009, 07:01 AM