Determining fixed wing aircraft AA and DF values

[cathar1244]

This series of comments provides a method of determining the anti-air (AA) rating and defense factor (DF) ratings for fixed-wing aircraft in TOAW. The method, at its most basic, determines the AA rating as a sum of the airframe performance and the air-to-air weapons effectiveness. Thus, three basic values have to be determined: the DF, the airframe performance rating, and the weapons effectiveness rating.

The method uses weights and calculations that appear arbitrary. These modifiers have been chosen in order to produce ratings that are compatible with the values in the standard TOAW equipment database.

A survey of the existing database reveals both the AA and DF values tend to range from 1 to around 60, except in the case of stealth aircraft, in which it appears 100 or so was arbitrarily added to the DF. The existing database values are compressed in the case of early aircraft. This was likely a consequence of these aircraft being fitted into the rating systems -- a system of ratings that was originally created for TOAW I, and only intended to rate aircraft of the period 1939 to 1955. A review of ratings in TOAW I shows, for example, the Polikarpov I-5 had an anti-air rating of 2 ... which didn't leave a lot of room for lesser ratings to depict older aircraft.

I intend to use this method to recalculate the fixed wing aircraft AA and DF ratings as part of a modified "chunk" of the equipment database. Until then, the method can be used to represent aircraft not present in the equipment database, such as the F/A-18E/F Super Hornet or the Eurofighter Typhoon. If anyone does not wish to use the method but would like to know what it assesses for a particular aircraft, they can post a request to this thread and we'll see what we can develop as a result.

(continues)

[cathar1244]

Step 1 -- gather aircraft data:

Service ceiling in feet
Maximum speed in miles per hour
Wing loading in pounds per square foot
An integer representing the effect of onboard radar, avionics, and fire control gear
How many men in the crew
The effect of air-to-air weapons (see weapons assessment sub-method)
The loaded weight in tons
The empty weight in tons
If the aircraft has a radar warning receiver
If the aircraft has a missile approach warning system
If the aircraft has countermeasures such as chaff or flares
Using the maximum speed, calculate the miles per hour per ton of loaded weight

continues ...

[cathar1244]

Step 2 -- keep this list of modifiers handy:

Arbitrary modifiers. Because the method has to rate aircraft of any era, modifiers were introduced to account for advances in aircraft construction and aircraft design.

Construction modifiers (to be applied to the miles per hour per ton of loaded aircraft.)

Code: Select all

 Decade in which produced	Factor
 
 1900				0.11
 1910				0.22
 1920				0.33
 1930				0.44
 1940				0.55
 1950				0.66
 1960				0.77
 1970				0.88
 1980				1.00
 1990				1.11
 2000				1.22
 2010				1.33
 

Design modifiers.

Code: Select all

 Factor				General design type
 
 0.5				Biplane or triplane
 0.6				Twin engines on wings
 0.5				Four or more engines on wings
 0.8				Straight wing monoplane
 0.9				Early swept back jets of the 1950s-1960s
 1.0				Modern aerodynamic design ( F-15, etc.)
 

[cathar1244]

Step 3 -- calculate the Defense Factor (DF)

Sub-method: Defense Factor assessment.

a. Determine empty weight in (2000-pound) tons (Da).
b. Aircraft durability (Db) is Da + ( SQRT (Da) / 2 ).
c. The radar and visibility cross section (Dc) is ( 1 / Da ) + 1.
d. Assign a value for the effectiveness of the radar warning system (Dd).
e. Assign a value for the effectiveness of the missile approach warning system (De).
f. Assign a value for the effectiveness of countermeasures (Dg).
g. Reckon the maximum speed in miles per hour divided by 100 (Dh).

DF = Dh + Db + SQRT (Dc) + Dd + De + Dg

Example. An Argentine IA-58 Pucara has an empty weight of 4.43 tons. This is Da.
Db = 4.43 + ( SQRT (4.43) / 2 ), or 5.48
Dc = ( 1 / 4.43 ) + 1, or 1.23
Dd, De, and Dg are assessed as 0 since the aircraft does not have these subsystems.
Dh = 311 / 100, or 3.11
DF = 3.11 + 5.48 + 1.11 + 0 + 0 + 0, which sums to 9.70 and rounds to 10.

At the moment, the method assumes Dd, De, and Dg are each equal to 7 for 1980s-1990s Western aircraft such as the F-15 Eagle and the F-18 Hornet. The magnitude of these values is judgmental.

continues ...

[cathar1244]

Step 4 -- assess weapons effectiveness

Sub-method: Air-to-air weapons assessment.

a. Determine the effect of a single projectile, including high explosives. (Wa)
b. Enter effective range in kilometers (Wb).
c. Range factor (Wc) equals 1 + SQRT ( 0.001 * Wb ).
d. Enter a reliability factor (Wd) in the range 0 to 1.
e. Enter an accuracy factor (Wf) in the range 0 to 1.
f. The basic weapon rating (Wg) equals Wa * Wc * Wd * Wf.
g. Determine the number of rounds fired by the weapon in 0.5 seconds (Wh)
h. The weight of fire (Wi) = Wg * Wh.

Perform steps a. through g. for all weapons and sum the weights of fire. This sum may be operated on to deliver results in a desired range. For the given database I am working with, I use the sum of the weights of fire (Wj) in this formula:

Weapons effectiveness (WE) = 3.721 * ( Wj raised to the power 0.381 )

Bear in mind WE will be added to the airframe rating to determine the anti-air factor. Altering how the weapons are assessed means one will have to review how the DF for the aircraft is determined lest one make the DF too strong or too weak by changing the weapons effectiveness.

Example. The NR-30 cannon is determined to have a Wa of 0.884 (a 400 gram projectile with associated explosive effects equivalent to a 0.884 Kilogram chunk of metal striking an airframe at high velocity).

Effective range of the NR-30 is judged as 600 meters (in air to air combat). This produces a Wc of 1.02. Wd (reliability) is judged as 0.8 and Wf (accuracy) as 0.7. Then,

Wg = Wa * Wc * Wd * Wf, or 0.505. Wh is 8 rounds in 0.5 seconds, producing a Wi of 4.04. Assuming this is the only air-to-air weapon, Wi = Wj, and WE = 6.33.

Air to air missiles are handled in a similar fashion except that the rounds fired in 0.5 seconds is always 1.

[cathar1244]

Step 5 -- assess airframe performance

Sub-method: Airframe assessment.

a. Divide the service ceiling in feet by 10,000. (Ab)
b. Divide the maximum speed in mph by 66.667. (Ac)
c. Divide the wing loading in pounds per square feet by 10. (Ad)
d. Multiply the mph per ton of loaded aircraft by the construction modifier (see Step 2).
e. Divide this adjusted mph per ton of loaded aircraft by 18. (Ae)
f. Determine a factor in the range 1 to 10 for the effectiveness of avionics etc. (Af)
g. If crew is more than 1, the crew factor (Ag) is equal to 1.2, else it is equal to 1.

The raw airframe assessment is calculated as:

( Ab + Ac - Ad + Ae + Af ) * Ag

This raw assessment is then multiplied by the design modifier (see Step 2):

AA = (raw_assessment * design_modifier)

Example. An F-16C has a service ceiling of 52,450 feet. Ab is then 5.245.
The maximum speed is given as 1,320 mph, so Ac is 19.80.
Wing loading is 88.3 pounds per square foot, so Ad is 8.83.
Avionics, fire control, and onboard radar are assessed as 7.
Crew is 1, so Ag is equal to 1.
The mph per (2000-pound) ton of loaded aircraft is 87.67.
This is adjusted by the construction factor of 0.88 (1970s era design).
The adjusted mph per ton of loaded aircraft is 77.15.
This adjusted figure is divided by 18, setting Ae to 4.29.

Raw score is ( 5.245 + 19.8 - 8.83 + 4.29 + 7 ) * 1, or 27.51
AA = 27.51 * 1 (the design modifier), or 27.51

To the value of AA must be added the weapons effectiveness.
Assuming this F-16 is equipped with the NR-30 cannon, the anti-air value is:

27.51 + 6.33, or 33.84 -- this rounds to 34.

[cathar1244]

Comments. There is a relationship between the three components of the method. Underlying this relationship is the assumption that the sum of AA and WE will not greatly exceed the value of the aircraft's DF. This relationship was established in the method to assure compatibility with the existing database. A designer may not consider this balance of values a priority and will feel free to alter the method as desired. Similarly, the formula that takes a raw weapons score and produces the value (WE) was shaped for compatibility with the existing database. The construction and design modifiers were introduced to smooth the effects of raw airframe evaluation. Without these modifiers, absurd results are generated, such as World War One aircraft approaching the effectiveness of mid to late World War Two fighters. Finally, the "miles per hour per ton of loaded aircraft" was used to evaluate how quickly the engine(s) could move an airframe, regardless whether the engine turned a propeller or generated a jet thrust.

Obviously, these calculations are far easier to make with the help of a spreadsheet. No doubt some designers will not agree with weights, calculations, or assumptions that make up this method. If nothing else, it can serve as a starting point for a different method of assessing fixed wing aircraft AA and DF.

If anyone finds this a useful tool for use in a scenario or custom database, it is requested you credit "cathar1244 on the Matrix forums" -- thank you.

Cheers

[mussey]

You've been busy Cathar! Very methodical, it should be very interesting to see what you come up with. What I like is that this should produce a uniform evaluation that can be fairly applied to all air equipments. I wonder if you will find any major discrepancies?

[cathar1244]

I wonder if you will find any major discrepancies?

Mussey,

I've done a handful of aircraft so far, and I consider the results "close enough" for TOAW's aggregate combat model. There are some discrepancies; my B-17G is rating stronger than the given database and my F-16C is less hot than the given database. It is hard to tell if these are errors (and their magnitude if so) because the original database was produced by a "black box" for which, I, at least, have no information. There is also the question of which values should be assigned for avionics, radar warning systems, and so forth, not to mention that I also have no idea how much weight the weapons rating played in creating the game's given equipment file ratings for anti-air capability.

I agree there is value in having a system to generate values that is documented as to how it functions. Even if people disagree about this value or that factor, at least they can specifically state about what they disagree. And since it generates values that are reasonably close to those in the equipment file, we can generate new types of aircraft and have at least some confidence that the ratings relate to those of other aircraft in the file.

At some point, it would be good to have a slightly simpler method that includes stock values like "four 1960s-era heat-seeking air-to-air missiles" instead of making the designer grind through the calculations.

As an aside, the anti-air missiles (ground or air launched) are IMO a mess to evaluate because there is so little information as to their ability to strike their targets. From what I've gathered, for all their sophistication, it still took something like 50 missiles to down a single aircraft in the Middle East conflicts of the 1970s and 1980s.

I also have a method that I'm finishing up for evaluating the anti-air ratings of AA guns and SAMs. It is similar to the weapons evaluation sub-method mentioned above.

Thank you for the comments.

Cheers

[cathar1244]

As a test today, I used the method to rate a Focke-Wulf 190A3. The method indicates an AA of 12 and a DF of 10. Method was filled out to indicate air to air weapons of two each MG/FF, MG151/20, and MG17.

Compares to:

Standard equipment file shows FW-190 (early) as 11 and 11.

The equipment file for FITE2 shows an A model FW-190 as 10 and 11.

So the method is easily in the ballpark.

In another thread, it was mentioned the Yak-7 is not in the standard equipment file.

Method shows the initial Yak-7 as 10 and 8, and the Yak-7B as 11 and 8. For comparison, the FITE2 equipment file shows the Yak-7B as 9 and 10. The method's uptick on the -7B was due to two 7.62-mm machine guns being replaced by two 12.7-mm machine guns.

Cheers

[larryfulkerson]

I really like what you're doing. Please keep up the good work. I think you've hit on
an excellent way to evalutate the different types of aircraft. I've got confidence in
the values you're getting. Excellent idea. Way to go.

[cathar1244]

Thanks, Larry. Believe me, I am not an aviation guy so I'm really stretching myself on this one. The biggest x-factor are the missiles and their effectiveness.

Cheers

[larryfulkerson]

Have you heard of the Janes Magazine? You can find it here:


https://www.janes.com/defence

I used to read the hardbound version many years ago and they went online and it's a lot more accessable now. They have hard data on all kinds of vehicles, aircraft, boats, missles, rockets, field guns, small arms, etc. And I like to peruse it for the pictures. They have all the up to date data on just about everything made for combat arms forces. I just found it a minute ago and thought you guys might like to hear about it too.

[StuccoFresco]

Amazing work.

[cathar1244]

Larry,

I am familiar with Jane's publications. I have a few of their works on my shelves, and yes, they are good for data like warhead weight, service ceiling, and such.

What is less easy to find is how effective complex systems like missiles are. I've got a kinda-sorta feel for it, but a lot of the data seems to contradict itself. 50 missiles per plane shot down in the Mideast Wars, yet North Vietnamese SAMs were a serious hazard for B-52s in Vietnam. Then there is a debate about the beyond-visual-range air to air missiles. The manufacturers, of course, claim they're wonder weapons, yet the targeted aircraft have their own defense mechanisms ... not to mention that BVR engagement wasn't used in Vietnam because of the fear of shooting down other friendly aircraft. The challenge is to try a balance in the TOAW ratings that feels realistic and doesn't throw the air combat system out of kilter.

Cheers

[larryfulkerson]

The challenge is to try a balance in the TOAW ratings that feels realistic and doesn't throw the air combat system out of kilter.

I detect a problem. The measure a player applies to the value of "balance"....it's subjective. It's opinion. It's probably going to be slightly different to each player according to their background, experiences, age, weight, gender, and bladder capacity. That last one because you may have to stand in a line for a long time in the near future. At any rate, it's going to probably be as hard as herding cats to get a confluence of opinion.

[cathar1244]

ORIGINAL: larryfulkerson

The challenge is to try a balance in the TOAW ratings that feels realistic and doesn't throw the air combat system out of kilter.

I detect a problem. The measure a player applies to the value of "balance"....it's subjective. It's opinion. It's probably going to be slightly different to each player according to their background, experiences, age, weight, gender, and bladder capacity. That last one because you may have to stand in a line for a long time in the near future. At any rate, it's going to probably be as hard as herding cats to get a confluence of opinion.

LOL, you're right about the number of points of view. At the moment, I've decided to boost (a bit) the firepower of newer missiles as the defense factor considers improvements in countermeasures etc. But any perceptions in how "good" a particular aircraft will be can be acted on by a scenario designer using a modified version of the definition in an scenario-unique equipment file.

One thing I've looked at to reduce subjective application of values is Moore's Law. My reasoning is that avionics have grown more powerful as the ability to pack electronic components into small spaces has grown. This approach will lend more standardization to values for on-board radar, missile approach warning systems, and so on.

My 'out of kilter' comment is more about the relationship of AA to DF in most of the aircraft definitions. Those two values are often close to each other. If that gets changed too much, it may result in aircraft that are too hard, or too easy, to shoot down. I will do some lab testing at some point to compare the standard database values and the values given by my method.

Cheers

[josant]

Cathar, under your point of view, and using your formulas, what would be the appropriate values of defense and anti air for the following aircrafts?

Mig-21
Mig-25
Mig-31
Mirage F1
Kfir
Cheetah
Lightning

[cathar1244]

Hi JosAnt,

Starting with the MiG-21. I chose to depict the MiG-21Bis. Aircraft modeled with:

* Twin-barrelled GSh-23 cannon
* Two AA-2C missiles
* Two AA-8 missiles
* Sirena radar warning receiver
* Flares and other passive countermeasures assumed
* On-board radar
* Design modification factor of 0.9 (1950s-1960s jet fighter)
* Construction factor of 0.77 (1960s construction)

Code: Select all

 
 Definition         Aircraft name         Anti-Air   Defense Factor
 
 Standard database  MiG-21 Fishbed        40         38
 
 My method          MiG-21Bis             36         28
 

There is a large difference in defense factor assessment. I am, however, skeptical of the standard equipment database in this case. It has the DF for an early MiG-21 as 27, but 38 for a later model. Now, what in terms of defensive systems could have pushed that rating up eleven points, or an increase of almost 50%?

I'll work the others you mentioned but it will take a day or so. I'll have to go down side-roads looking up the weapons and assessing them.

Cheers

Note: Data source for MiG-21 was Greg Goebel's excellent website: https://www.airvectors.net/avmig21_1.html#m4

[cathar1244]

MiG-25: I chose to depict the MiG-25PD ("Foxbat-E"). Aircraft modeled with:

* Four AA-6 missiles
* Sirena radar warning receiver
* Flares and other passive countermeasures assumed
* On-board radar
* Design modification factor of 1.0 (modern jet fighter)
* Construction factor of 0.88 (1970s construction)

Code: Select all

 
 Definition         Aircraft name         Anti-Air   Defense Factor
 
 Standard database  MiG-25 Foxbat         25         38
 
 My method          MiG-25PD              47         50
 

Big differences in this case. I don't understand why the standard database rates the -25 relatively weakly. This aircraft was very fast, holds the world's altitude record, and was equipped with four of the heaviest air-to-air missiles ever developed.

Cheers

Note: Data source for MiG-25 was again Greg Goebel: https://www.airvectors.net/avmig25_1.html#m2