JG14_Josf

06-03-2004, 03:06 PM

The following is an attempt to make sense of the world where fighter planes exist.

The title of the topic is a formula as it appears in the book BOYD The Fighter Pilot who changes the art of war by Robert Coram.

That formula is not written the same as it appears in Fighter Combat by Robert Shaw.

The subtle difference are curious, I think, based upon my resent inspection of the properties of inertia, mass, and relative density.

A plane with a higher mass, higher inertia, and higher relative density compared to a plane with lower mass, lower inertia, and lower realative density will react differently to the medium which resists the planes movement i.e. the atmosphere.

Moving the heavier plane requires more energy and releasing that energy once it is gained is formulated by the equation: Ps=[T-D/W]V.

My question concerns math.

Is this a true mathematical statment:

[T-D/W]= T/W - D/W

Take a P-47 and a Bf109K and consider a few things concerning this plane matchup. First, for the purposes of this discussion, let's imagine that these two planes have the same level max speed. If it would help then consider that these planes are not production models that instead they are custom. They both have the same level max speed at 8k meters. Now imagine that the P-47 is twice the weight of the Bf109K. Bear with me here, if you are at all interested in this stuff, my point concerns something specific so it is important to avoid getting caught up in exact plane performance numbers.

The P-47 and Bf109 are flying side by side at the same max level speed.

What happens when both planes are pitched up from that level flight condition?

What happens when both planes are pitched down from that level flight condition?

Mass and or inertia is going to resist any changes in pitch more so with the heavier P-47 than with the Bf109.

Gravity is a constant force applied to these two planes as they fly level, however these two planes are not going to be able to deal with the force of gravity in the same way due to their differences in mass, among other things.

The P-47 has enough thrust and lift to maintain an equal velocity in level flight but in order for the P-47 to gain anymore altitude from this position of equalibrium it will require more thrust and or more lift than the Bf109 because the P-47 has more mass and therefore is more susceptible to the force of the earths gravity. The higher mass of the P-47 requires more energy to move it against the force of gravity.

Since the P-47 and Bf109 are already at max thrust in max level flight then as these two planes pitch up the 109 will require less lift to change direction and less lift to resist the force of gravity to lift it higher, or accelerate against the force of gravity.

Due to relative mass the Bf109 is going to have better climb performance.

In order to see clearly what happens when both planes pitch down it is now important, at least to me, to consider the medium which resists movement or air and the effects of relative density.

Both planes accelerate at the same speed due to the force of gravity in a vacuum. Air hinders this rate of acceleration. This resistance is termed drag, and it is described as a force. Drag force is equal to thrust when both planes are flying level at max speed.

Here comes the important point and the reason for the mathematical question concerning the Specific excess power equation.

As an objects mass increases it becomes relatively more able to pass through a medium of resistance. Mass renders drag less effective. Drag force is more capable of resisting the movement of a lower mass object.

To make this point more clear consider what happens to top level speed for a plane that gains weight.

Chapter 5 Excess Power Characteristics (http://flighttest.navair.navy.mil/unrestricted/FTM108/)

Page 5.14

5.3.5.2 INCREASED GROSS WEIGHT

"The effect of increasing gross weight is similar to that of increasing the normal acceleration, with the difference that both the numerator and denominator are affectd rather than the numberator alone (Figure 5.8):"

and Page 5.15

"The balance of thrust and drag is the same, resulting in identical minimum and maximum level flight speeds."

If it is true that increases in weight do not lower max level flight speeds then it seems clear to me that this is due to a change in relative density.

The air is rendered comparitaively or relatively less dense as the mass of the object passing through the air is increased.

Thrust does not change on the plane as it increases weight. More lift is required to stay level when weight is added and therefore more induced drag is generated. Why does the plane still fly at the same speed when adding weight? It seem clear to me that the total force of drag is the same because the plane does not accelerate. Thrust remains constant, induced drag increases, weight increases, and velocity remains the same. I think that the higher mass plane is more capable of penetrating the atmosphere. The increase in the planes density renders the air relatively less dense.

Chapter 8 DEscent Performance (http://flighttest.navair.navy.mil/unrestricted/FTM108/)

Page 8.7 WEIGHT EFFECT ON DESCENT PERFORMANCE

"At the higher airspeed for the higher gross weight, the increase in drag is offset by the increased weight component along the flight path.":

In level flight the P-47 and the Bf109 both have enough thrust to counter the force of drag (they are both at the same max speed) they both have the same balance between weight and lift (level flight). However the P-47 has a higher mass. The increased mass required more energy to get the vehicle moving and more energy to get to that same altitude. Therefore the P-47 has more energy despite being at the same speed and same altitude. If it is reasonable to conclude that the P-47 will perform relatively poorly as both planes change direction from level flight to a climb because the mass is both more difficult to move and more difficult to lift then what can be said about any change from level flight into a dive?

Conventional thinking has been previously expresses that the P-47 will not accelerate any faster and possibly accelerate slower than the lighter Bf-109 in a dive due to the difficulties associated with moving objects of higher mass. To further complicate the matter it has also been stated that since gravity accelerates all objects at the same rate regardless of weight in a vacuum that both the P-47 and the Bf109 will dive at the same rate, much like what occurs in previous versions of the game. One more complication concerning dive performance has been described as a simple equation where the greater mass vehicle will accelerate slower up to max level speed (in a dive) and above the level max speed the situation reverses where the higher mass vehicle accelerates faster than the lower mass one, in a dive.

Before moving on to the situation where the higher mass vehicle accelerates slower than the lower mass vehicle at speeds below max level speed it may help to look at what happens when two imaginary planes are flying at the same max level speed where one plane has an obviously higher mass.

Back again to the Bf109 and the P-47 flying level at full power where for whatever imaginary configuration these planes are maxed out at the same speed.

Both planes pitch over in a dive.

Gravity is a constant force generated by the earth and this force accelerates both planes at the same rate but only in a vacuum. Since an atmosphere is present and since this form of resistance does limit the acceleration of these vehicles as they are being accelerated by gravity then it is neccesary to measure that form of resistance in an effort to find just how effective that resistance is when acting upon our vehicles.

One such method of measuring the resistance to movement presented by the atmosphere is to quantify density. The higher the density of the atmosphere the greater will be the drag force acting against movement. The lower the density of the atmosphere the lower will be the drag force acting against movement.

Before moving any further it occurs to me to return to the observation of a plane's max level speed and the associated effect of changes in mass. Imagine that the P-47 is filled with mercury, it has a much more powerfull engine to move this increased mass and it has larger, more effective wings to lift this increased mass against the force of gravity. The P-47 is still flying at the same max level speed as the Bf109. Both planes are flying side by side, both planes still have a balance between thrust and drag, lift and gravity. Now imagine that the P-47 dumps the mercury. It is reasonable to conclude that as the mercury is dumped the P-47 will climb if the pilot does not push the stick forward. For the purposes of this discussion it is required that the pilot push the stick forward in an effort to maintain level flight. The reason why this piloting is required is for us to realize what forces are in place that cause any change in max level flight velocity.

Before moving on it is important to indentify what happens in this situation.

It is important to identify why the P-47 is not able to gain any more level flight speed as the P-47 reduces mass.

Picture the P-47 crusing alone in a race with the Bf109. Both pilots are trying to win the race to the finish line. The P-47 happens to be burdened with a cargo of mercury and he thinks it would help to dump the cargo. He does so thinking that he will then be able to speed ahead and win the race.

Who wins the race?

Because I find reason to write and because this subject interests me I am going to move ahead without confirmation of the results of the above race between an imaginary Bf109 and a special high mass P-47. I am going to move on with the assumption that the P-47 will not win the race as it dumps mercury and decreases mass.

I want to bring this line of thinking back to the Specific Excess Power formula.

T/W - D/W suggests to me that weight can be factored relative to drag so as to account for relative density.

That is it for now.

OOOPs I forgot a note of relevance.

On Warclouds I found myself flying alone. My normal wingmen were all busy with real life things. A P-38 zoomed by from about 10 degrees angle off my nose or 1 oclock high. Since then I checked the replay to see how this guy managed to avoid detection and I found that his P-38 was hidden behind the forward up right canopy bars. I went into a dive after being bounced by the P-38. My thinking was that the P-38s will break apart in the game at lower speeds than my 109G6AS. I can therefore gain relative energy. Sure enough the separation grows and I start pulling up into a climb. My thinking was that the game allows the AS to gain in relative energy over the P-38 in a sustained climb.

The text buffer says:

"Timid 109s diving and climbing"

or something to that effect

I reply:

"<S>" etc.

I've stood under a P-38. It is a large plane. There was one at the Chino air museum along with a Rolls engined Bf109. There is another Bf109 at the Planes of Fame museum in Flagstaff Arizona. I saw that one too.

I can stand next to the 109s and see the instrument panel. I am 6 feet tall.

The 109 is a small plane.

Each of us have our own opinions as to what should or should not be done in Air Combat. I try to fly to my planes strengths. I also try to simulate what has been written in history books. Sometimes I succeed. Somtimes I have to take flak for it.

The title of the topic is a formula as it appears in the book BOYD The Fighter Pilot who changes the art of war by Robert Coram.

That formula is not written the same as it appears in Fighter Combat by Robert Shaw.

The subtle difference are curious, I think, based upon my resent inspection of the properties of inertia, mass, and relative density.

A plane with a higher mass, higher inertia, and higher relative density compared to a plane with lower mass, lower inertia, and lower realative density will react differently to the medium which resists the planes movement i.e. the atmosphere.

Moving the heavier plane requires more energy and releasing that energy once it is gained is formulated by the equation: Ps=[T-D/W]V.

My question concerns math.

Is this a true mathematical statment:

[T-D/W]= T/W - D/W

Take a P-47 and a Bf109K and consider a few things concerning this plane matchup. First, for the purposes of this discussion, let's imagine that these two planes have the same level max speed. If it would help then consider that these planes are not production models that instead they are custom. They both have the same level max speed at 8k meters. Now imagine that the P-47 is twice the weight of the Bf109K. Bear with me here, if you are at all interested in this stuff, my point concerns something specific so it is important to avoid getting caught up in exact plane performance numbers.

The P-47 and Bf109 are flying side by side at the same max level speed.

What happens when both planes are pitched up from that level flight condition?

What happens when both planes are pitched down from that level flight condition?

Mass and or inertia is going to resist any changes in pitch more so with the heavier P-47 than with the Bf109.

Gravity is a constant force applied to these two planes as they fly level, however these two planes are not going to be able to deal with the force of gravity in the same way due to their differences in mass, among other things.

The P-47 has enough thrust and lift to maintain an equal velocity in level flight but in order for the P-47 to gain anymore altitude from this position of equalibrium it will require more thrust and or more lift than the Bf109 because the P-47 has more mass and therefore is more susceptible to the force of the earths gravity. The higher mass of the P-47 requires more energy to move it against the force of gravity.

Since the P-47 and Bf109 are already at max thrust in max level flight then as these two planes pitch up the 109 will require less lift to change direction and less lift to resist the force of gravity to lift it higher, or accelerate against the force of gravity.

Due to relative mass the Bf109 is going to have better climb performance.

In order to see clearly what happens when both planes pitch down it is now important, at least to me, to consider the medium which resists movement or air and the effects of relative density.

Both planes accelerate at the same speed due to the force of gravity in a vacuum. Air hinders this rate of acceleration. This resistance is termed drag, and it is described as a force. Drag force is equal to thrust when both planes are flying level at max speed.

Here comes the important point and the reason for the mathematical question concerning the Specific excess power equation.

As an objects mass increases it becomes relatively more able to pass through a medium of resistance. Mass renders drag less effective. Drag force is more capable of resisting the movement of a lower mass object.

To make this point more clear consider what happens to top level speed for a plane that gains weight.

Chapter 5 Excess Power Characteristics (http://flighttest.navair.navy.mil/unrestricted/FTM108/)

Page 5.14

5.3.5.2 INCREASED GROSS WEIGHT

"The effect of increasing gross weight is similar to that of increasing the normal acceleration, with the difference that both the numerator and denominator are affectd rather than the numberator alone (Figure 5.8):"

and Page 5.15

"The balance of thrust and drag is the same, resulting in identical minimum and maximum level flight speeds."

If it is true that increases in weight do not lower max level flight speeds then it seems clear to me that this is due to a change in relative density.

The air is rendered comparitaively or relatively less dense as the mass of the object passing through the air is increased.

Thrust does not change on the plane as it increases weight. More lift is required to stay level when weight is added and therefore more induced drag is generated. Why does the plane still fly at the same speed when adding weight? It seem clear to me that the total force of drag is the same because the plane does not accelerate. Thrust remains constant, induced drag increases, weight increases, and velocity remains the same. I think that the higher mass plane is more capable of penetrating the atmosphere. The increase in the planes density renders the air relatively less dense.

Chapter 8 DEscent Performance (http://flighttest.navair.navy.mil/unrestricted/FTM108/)

Page 8.7 WEIGHT EFFECT ON DESCENT PERFORMANCE

"At the higher airspeed for the higher gross weight, the increase in drag is offset by the increased weight component along the flight path.":

In level flight the P-47 and the Bf109 both have enough thrust to counter the force of drag (they are both at the same max speed) they both have the same balance between weight and lift (level flight). However the P-47 has a higher mass. The increased mass required more energy to get the vehicle moving and more energy to get to that same altitude. Therefore the P-47 has more energy despite being at the same speed and same altitude. If it is reasonable to conclude that the P-47 will perform relatively poorly as both planes change direction from level flight to a climb because the mass is both more difficult to move and more difficult to lift then what can be said about any change from level flight into a dive?

Conventional thinking has been previously expresses that the P-47 will not accelerate any faster and possibly accelerate slower than the lighter Bf-109 in a dive due to the difficulties associated with moving objects of higher mass. To further complicate the matter it has also been stated that since gravity accelerates all objects at the same rate regardless of weight in a vacuum that both the P-47 and the Bf109 will dive at the same rate, much like what occurs in previous versions of the game. One more complication concerning dive performance has been described as a simple equation where the greater mass vehicle will accelerate slower up to max level speed (in a dive) and above the level max speed the situation reverses where the higher mass vehicle accelerates faster than the lower mass one, in a dive.

Before moving on to the situation where the higher mass vehicle accelerates slower than the lower mass vehicle at speeds below max level speed it may help to look at what happens when two imaginary planes are flying at the same max level speed where one plane has an obviously higher mass.

Back again to the Bf109 and the P-47 flying level at full power where for whatever imaginary configuration these planes are maxed out at the same speed.

Both planes pitch over in a dive.

Gravity is a constant force generated by the earth and this force accelerates both planes at the same rate but only in a vacuum. Since an atmosphere is present and since this form of resistance does limit the acceleration of these vehicles as they are being accelerated by gravity then it is neccesary to measure that form of resistance in an effort to find just how effective that resistance is when acting upon our vehicles.

One such method of measuring the resistance to movement presented by the atmosphere is to quantify density. The higher the density of the atmosphere the greater will be the drag force acting against movement. The lower the density of the atmosphere the lower will be the drag force acting against movement.

Before moving any further it occurs to me to return to the observation of a plane's max level speed and the associated effect of changes in mass. Imagine that the P-47 is filled with mercury, it has a much more powerfull engine to move this increased mass and it has larger, more effective wings to lift this increased mass against the force of gravity. The P-47 is still flying at the same max level speed as the Bf109. Both planes are flying side by side, both planes still have a balance between thrust and drag, lift and gravity. Now imagine that the P-47 dumps the mercury. It is reasonable to conclude that as the mercury is dumped the P-47 will climb if the pilot does not push the stick forward. For the purposes of this discussion it is required that the pilot push the stick forward in an effort to maintain level flight. The reason why this piloting is required is for us to realize what forces are in place that cause any change in max level flight velocity.

Before moving on it is important to indentify what happens in this situation.

It is important to identify why the P-47 is not able to gain any more level flight speed as the P-47 reduces mass.

Picture the P-47 crusing alone in a race with the Bf109. Both pilots are trying to win the race to the finish line. The P-47 happens to be burdened with a cargo of mercury and he thinks it would help to dump the cargo. He does so thinking that he will then be able to speed ahead and win the race.

Who wins the race?

Because I find reason to write and because this subject interests me I am going to move ahead without confirmation of the results of the above race between an imaginary Bf109 and a special high mass P-47. I am going to move on with the assumption that the P-47 will not win the race as it dumps mercury and decreases mass.

I want to bring this line of thinking back to the Specific Excess Power formula.

T/W - D/W suggests to me that weight can be factored relative to drag so as to account for relative density.

That is it for now.

OOOPs I forgot a note of relevance.

On Warclouds I found myself flying alone. My normal wingmen were all busy with real life things. A P-38 zoomed by from about 10 degrees angle off my nose or 1 oclock high. Since then I checked the replay to see how this guy managed to avoid detection and I found that his P-38 was hidden behind the forward up right canopy bars. I went into a dive after being bounced by the P-38. My thinking was that the P-38s will break apart in the game at lower speeds than my 109G6AS. I can therefore gain relative energy. Sure enough the separation grows and I start pulling up into a climb. My thinking was that the game allows the AS to gain in relative energy over the P-38 in a sustained climb.

The text buffer says:

"Timid 109s diving and climbing"

or something to that effect

I reply:

"<S>" etc.

I've stood under a P-38. It is a large plane. There was one at the Chino air museum along with a Rolls engined Bf109. There is another Bf109 at the Planes of Fame museum in Flagstaff Arizona. I saw that one too.

I can stand next to the 109s and see the instrument panel. I am 6 feet tall.

The 109 is a small plane.

Each of us have our own opinions as to what should or should not be done in Air Combat. I try to fly to my planes strengths. I also try to simulate what has been written in history books. Sometimes I succeed. Somtimes I have to take flak for it.