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Structural Sub-Component Weight Groups Parametric Plots

The plots below show some of the preliminary parametrics for the sub-component weights that sum to the Overarching Structural Group weight that have been developed from the data available for single engine monoplane WWII era aircraft discussed on this website.  

Caveats
Please note that; 
  1. Currently everything is still very much a work in progress and subject to further refinement and revision as I work to verify the data that I have currently transcribed from the references, and as I work to collect dimensional and powering data on the specific aircraft that I have weight data for.
  2. All weight units are in pounds and power units are in Horsepower.
  3. For some weight groups (such as the "Tail" group or the "Landing Gear" group, a further subdivions of weights may be provided for those airplanes where such data was available.  As such, rows below the "Tail" group for the "H Tail" (Horizontal Tail) and "V Tail" (Vertical Tail) are included for some aircraft.  Similarly rows below the "Landing Gear" group for "Main LG" and "Tail/Nose Aux LG" have also been added, though I may eventually separate the "Tail/Nose Aux LG" row into a separate "Nose Aux LG" and "Tail Aux LG" row to make it easier to differentiate these weights on the parametric plots being developed.
  4. It currently is unclear what all is included in the "Engine Section" weight group.  It appears that this includes the the engine mounts for allaircraft as well as cowling and cooling flaps for radial engines. However for a few aircraft in the lists below such as the XP-63A a very low value of 4lb is given, while for the P-63A-10 and P-63C no value is given, leading to the suspicion that the weights of the enine mount for those aircraft may be included elsewhere in the weight estimate (such as in the "Fuselage" weight or "Engine Accessories" weight groups.
  5. I need to further review and clean up the "Fuselage" and "Body" group weights to ensure that I have correctly and consistantly recordedd this data.  Specifically;
    1. In Reference [1] many of the aircraft list "Fuselage" and "Engine Section" weights separately.  However for several of the F2A/B339 aircraft variants a "Body + Landing Gear" weight and an "Engine Section" weight is given, whereas for the XF2A-1 no separate "Engine Section" weight appears to be given. 
    2. In Reference [2] only "Body" weights are listed, with no mention of "Fuselage" or "Engine Section" weights.
    3. In References [3] and [4] the "Body Group" weight is listed as including the "Fuselage less Engine Section" and "Alighting Gear" (Landing Gear).  However, since weight data is provided for both the  "Fuselage less Engine Section" and "Alighting Gear" in addition to the total "Body Group" weight it is fairly easy to re-align these weights to match the format used in other references if necessary.  However, eventhough the "Fuselage less Engine Section" is called out as a weight group I cannot find anywhere in these references where the "Engine Section" is accounted for.  As such, I am currently still reviewing the weight from these two references and have not yet incorporated them into the plots below.
    4. In Reference [5] the "Body Group" weight and "Landing Gear" weights are listed separately.
As such, it appears that the most consistent use of terminology would be to;
  1. Treat the "Body Group" as being the sum of the "Fuselage" and "Engine Section Groups"
  2. Investigate the weights of the "Alighting Gear" (Landing Gear) separately, where possible
  3. Also dosome analyses of "Body" weight plus "Landing Gear" weight to see how the F2A/B339 variants listedin Reference [1] compare to the other aircraft that there is data on.
Beyond this I also intend to continue to review the information provided in References [3] and [4].

Structural Weight Sub-Components

As noted on the General Weight Summary Format page, the overarching Structural Weight Group is equal to the sum of the;
 Wing Group

The first plot below show the relationship of Wing Weight to Total Wing Area.  As shown in this plot a number of the naval aircraft designs have folding wings.  

Wing_Wt_1

I am currently working to try and develop more detailed plots to better help identify the impact that incorporating the ability to fold has on the overall weight of a wing. In addition, in reviewing Wing Weight equations for other aircraft type it can be seen that there are several other factors other than just Wing Area which are expected to impact the overall wing weight, including such factors as;
 In the paper "A Review of Aircraft Wing Mass Estimation Methods" by Odeh Dababneh amd Timoleon Kipouros [Reference 19], a figure is provided for more modern aircraft plotting Wing Weight versus a parameter equal to;
The Aircraft's Gross Weight * Ultimate Load Factor (in G's) * Wing Span * Gross Wing Area / Wing Thickness @ the Root

Plotting the weight information available for WWII era Aircraft against the same parameter (assuming pounds for weight and feet or feet squared for the other dimension, as appropriate) results in the plots shown below, where the first graph shows the data on a log-log scale and the second plot shows the data on normal X and y scales.

Rev Wing Wt

Rev Wing Wt 2

In these graphs please note that aircraft with fixed wings are shown as solid symbols while those with white centers represent aircraft with foldable wings.  As shown in these figures although there is some scattter the fixed wing data shows a reasonable fit (R2= 0.9043) with the data for aircraft showing a slightly weaker fit (R2= 0.7708).  However, it should be noted that some assumptions were made in the data.  Specifically;for aircraft where
Additionally, for the Brewster 239/XF2A-1 Prototypes, where a Normal Design Load Factor of 9 G's is known and a ration of Ultimate to Yeild Strngth of 1.35 is also provided, the Ultimate Load Factor was assumed to by 12.15 G's (or 1.35 * 9 G's). 

Some concerns here are that;
With respect to the Ultimate Load Factors for different variants of an aircraft, it is noted that in Ref X for the Curtiss Hawk H-75A when fitted with a Curtiss Wright Cyclone Engine having a Basic Gross Mission Weight o 5562lb is listed as having an Ultimate Load Factor of 12 G's, while the dsame design, but fitted with a Pratt & Whitney Twin Wasp engine and having a Basic Gross Mission Weight of 5792lb is listed as having an Ultimate Load Factor of 11.5 G's (where 5562lb * 12 G's ~= 5792lb * 11.5 G's).

Folding Wings

With respect to folding wings, NASA Report N81-23068  "Aircraft Wing Weight Build-Up Methodology With Modification for Materials and Construction Techniques" by Peter York and Raymond W. Labell dated September 1980 [Reference 20], provides the follwing formula for estimating the weight penalty for folding (or pivoting) wings based on post WWII aircraft;
Wt Penalty = 0.03386 * (B * n) *^ 0.2477 * (Sw) ^ 1.244 * ( 1 - b'/b) ^ 1.307 * Kws
where;
B = Maximum Clean Gross Weight or nlaximum Zero Wing Fuel Weight (lb)
Less:
    Wing Croup Wing
    Fael (Amount in above gross weight)
    Main landing gear if in the wing
    Nacelle Group if in the wing
    Propulsion Group if engines are in the wing
    Electrical Group if engines are in the wing
    Oil and Unusuable Fuel if engines are in the wing
n = Ultimate load factor at FDGW (for maneuver)
Sw = Wing Area (sq ft)
b' = Folded wing span or pivot span for variable sweep (ft)
b = Wing Span (ft)
Kws = 1.0 for Folding Wings or 0.556 for Variable Sweep Wings

Additionally the paper "The method of the folding wing’s design and mass optimization for the naval aircrafts" by Yarygina Maria Viktorovna of the Moscow Aviation Institute [Reference 21] provides a method for estimating the weight impact of fitting folding wings on modern Russian naval aircraft, and the presentation "Mass Estimation of Folding Wings" by Dieter Scholz Vladimir Zhuravlev Hamburg University of Applied Sciences Moscow Aviation Institute [Reference 22] provides a re-analysis of this data to develop an estimation method based on the transverse location of the wing fold mechanism along the wing span, providing the following equation;
Relative Mass Increase = mfold = mins + mmech,fold + mmech,pin
=-0.659 y/(b/2) + 0.659

For reference, based on the data I currently have available for the fixed wing F4F-3, and the folding wing F4F-4 and FM-2 varaints of the Wildcat fighter, the fold mechanism for the F4F-4 and FM-2 appears to be at a half-span of approximately 51 in from centerline while the overall half-span of the wing is 228 inches, for a y/(b/2) of 22.4%. 

Based on the equation from Reference 20 the estimated weight penalty for folding wings for the Wildcat type figher would be 380 to 395 lb (or a 42-44% increase).

Based on the equation from Reference 22 the estimated weight penalty for folding wings for a Wildcat type fighter would be 51% (or about 450 to 460 lb increase).

Based on the weight data available for the F4F-3, F4F-4/Martlet I/FM-1 and the FM-2 the actual weight increase between the F4F-3 and the FF4F-4/Martlet I/FM-1 would be between 225 to 340lb (or a 25 to 39% increase
) while the increase from an F4F-3 to the FM-2 would be 260 to 272 lb (or about 29 to 31%).

It appears that the equations from References 20 and 22 likely include the weight of hydraulics that may be fitted on more modern aircraft but which was not present on the WWII era Wildcat fighters, which may represent some of the wdifference in the estimated weights.  A review of Reference 21 indicates that the weight of the hydraulic actuators.

Trainer Aircraft

Unfotunately in the above wing weight re-analysis, I was not able to include the infromation that I have available on trainer aircraft, due in part to the limited information that I currently have available on the ultimate load factors they were designed to.  As such, I have plotted those weights against wing area to try and develop a simpler estimate for their weights, as shown in the plot below.  In these plots I have included the Soviet Post WWII era Yake-11 and the US WWII era Biplane PT-13A only for reference, and they were not used to develop the trend lines shown.  As shown in the first plot most of the data for the US WWII era monoplane trainers fall reasonably closely to the trend line, with the largest outlier ppearing to the the AT-19.  Of note, all the trainers listed escept the AT-19 were two-seat low-wing aircraft, primarily used for training pilots and air gunners, while the AT-19 was a high-wing 3 seat aircraft primarily used for training observers and navigators.  As such, AT-19 has some notable differences from the other trainer aircraft shown.  The second plot below shows a revised trend line for only the two-seat aircraft with the other data points removed for cllarity.

Trainer-Wing-Wt

Trainer-Wing_Wt2

Tail Group

The next three plots show the relationship of Total Tail Weight to Total Tail Area, Horizontal Tail Weight to Horizontal Tail Area, and Vertical Tail Weight to Vertical TailArea, respectively.  

Tail_Wt_2

H_Tail_Wt_2

V_Tail_Wt_2

Body Group

These last few plots show "Body Group" weight versus both "Basic Mission Gross Weight" and "Body Length".  In reviewing the data though, it is not clear what the "Body Length" reported in Reference [2] specifically relates to.  Specifically for radial engined aircraft it looks like it may actually only address to length of the aircraft aft of the fire wall, and not include the length of the cowling.  As such I intend to further review these values and may eventually replace the plot below with a plot of "Body Weight" versus "Total Aircraft Length".  Also along these lines, since there appears to be some degree of scatter in the plot of "Body" weight verse "Body Length" I may look to trying to also incorporate "Body Width"and "Body Depth" into the analyses since the weight of a very deep fuselage or a very narrow fuselage may be expected to vary a fair bit from other aircraft of similar lengths.

Body_Wt_1

Body_Wt_2

Landing Gear Group

The next three plots show the Total Landing Gear Weight, the Main Landing Gear Weight, and the Nose/Tail Landing Gear Weight as a function of the Basic Mission Gross Weight of the aircraft analysed.

LG_Wt

Main_Landing_Gear_Weight

Auxliary_LG_Wt

Due to the scatter in the above plots I decided to try and develop more detailed estimation methods for both the main and auxiliary landing gear weights.  For the auxiliary landing gear I separated the data first into those with nose mounted auxiliary landing gear (such as the P-39 and P-63) and those with tail mounted landing gear (which included the rest of the aircraft that I currently have data for).

Due to the limited data that I currently have for aircraft with tricycle type landing gear I have not yet been able to develop curves or trend lines for the weight of the nose gear for those type aircraft.

For tsil dragging aircraft I seoarated the data into a number of broad categories depending on if the tail wheels were fixed (in the down position), semi-retractable, fully retractable, and fully retractable with hinged doors enclosing them when retracted. and replotted the data as shown below.

Tail_Wheel_Wt

As shown in the figure above much of the data falls relatively closely to three curves, with the aircraft with "Fixed" tail wheels falling along the lower (Blue) curve.  Next, the aircraft with steerable tail wheels fixed in the down position and those with retractable landing gear (but not separate hinged doors) all appear to fall along the middle (Orange) curve.  And finally, the aircraft with retractable tail wheels and hinged doors, appear to fall mostly along the upper (Purple) curve.

In geeneral I am still working to verify all the information but the aircraft with fixed landing gear that I have data on includes;
 The aircraft with fixed but steerable tail wheels includes;
 The aircraft with retractable tail wheel (but not hinged doors) includes;
 And finally, the aircraft with retractable tail wheels and hinged doors includes;
 Tail_Wheels
[Source: Ref 8 (as annotated by this site)]

It should be noted that all this data has not yet been fully verified as some naval aircraft could either be fitted with hard rubber, retractable wheels for use on carriers but also be retrofitted with larger inflatable, non-retractable tail wheels when operated from land, and it is not always fully clear which configuration the available weight data represents.   In addition for land based versions of carrier capable aircraft types, it is not fully clear if all the retractable mechanisms and equipment was removed from these land based variants or whether only the wheels, tires and related bottom end support structure was altered (to potentially allow for a quick revision back to a smaller hard rubber retractable wheel if necessary.

For the main landing gear I have attempted to collect data to relate these weights not just to an aircraft's Basic Mission Gross Weight but also the length of the main landing gear strut/mechanism (from its upper attachment point to the aircraft's structure to the main wheel axle (as shown below), as well as the main landing gear wheel diameter. 

P51LG
[Source: Ref 16 (P-51 Dwg 102-33001)]

With this data I performed a regression analysis in Excel for the land based aircraft and the naval aircraft spearately.  The graph below shows a plot of the estimated main landing gear weight for the aircraft analysed versus the actual weights.  In general this graph shows a little bit of scatter but overall appears to show a pretty good level of agreement.

MLG_Comp

The equations developed from these regression analyses are as follows;

Land Aircraft:
Mn Landing Gear Wt (lb) = -175.002 + 0.023254 * BMGW + 12.62256 * MLG-Length + 1.262165 * MLG Tire Diameter

Naval Aircraft:
Mn Landing Gear Wt (lb) = -1242.26 + 0.013049 * BMGW + 6.093593 * MLG-Length + 42.56083 * MLG Tire Diameter


Notes: This website has been developed with a number of low cost or free programs including Hot Metal Pro, KompoZer, Microsoft Designer and Da Button Factory.com

Rev 5-11-26
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