Airplanes in 3D

In the previous post in this blog I described the state of my P-40 model at the end of 2020. In that time, I was missing information about its propeller blades. Ultimately I identified the two propeller variants used in the early P-40 (up to the P-40C version): first batches used hollow steel blades, while in the later aircraft they were made from solid dural. I expected that sooner or later I will find new information about their geometry, so I left their meshes in the ready for further modifications (see Figure ‎124‑5 in the previous post).

Three years later I exchanged some materials about various aircraft with a modeler from Ukraine. Among them there were three inconspicuous images:

It looks like a scan of an unidentified printed material (a book?). I can read it, so I quickly learned that tables a) and b) describe blade geometry of the Curtiss “Tomahawk” propellers. Image a) describes its duraluminum variant, while image b) – the hollow steel version. Image c) depicts the measurement scheme and explains the meaning of the columns from these tables.

Each row of the tables from a) and b) describes a single section of the blade, located at R (in mm) from the propeller axis of rotation. Provided data allows you to determine its size, position and rotation, but tells nothing about the airfoil shape. You can calculate the distance along the airfoil chord between the blade axis and the leading edge from the proportion b1/B = a1/A , which leads to b1 = a1*B/A. However, there is no clue about its vertical equivalent, marked in Figure ‎125‑1c) as c1. We know the overall thickness of the blade airfoil at this station (c) but have no information about the elevation of its chord line. It seems that the authors of these measurements assumed that the bottom contour of the blade airfoil is always flat. This can be true in the case of the Curtiss propeller from the P-40, but false in the case of some other aircraft, for example – Heinkel He-111.

The short single-row tables at the top of Figure ‎125‑1a) and b) provide the propeller diameter (D, in meters), twist angle (φ0) at station R = 1000 (mm), distance from the blade tip to the base plate, deviation of the blade tip from the blade axis, and distance between blade axis and the base plate. (According to Figure ‎125‑1c).

Can we use such data from an unidentified source? Well, these pages seem authentic. The Soviet Union always thoroughly analyzed each piece of the armament it received. Between 1939 and 1941, during the alliance with the German Third Reich, they received and documented various aircraft used by the Luftwaffe, like the Messerschmidt Bf 109E or Bf 110C. After June 1941 they did the same with the Lend-Lease weapons. Then they use this data as examples in their guide books for the aviation engineers. This can be a fragment of one of these guides.

For example: in the key Soviet guide for the aviation engineers from the 1943, most cutaway drawings depicting details of the stressed-skin aircraft structures shows German planes. I suppose that they were treated as “safe” by its authors, while a cutaway of a modern Soviet aircraft would be immediately discarded by the censors (and you could be accused of revealing military secrets).

Anyway, as the ultimate test we can always match the shape of the blades, formed according to tables from Figure ‎125‑1, against the reference photos (see Figure ‎124‑6 in the previous post). So, let’s try to make use of this data and see what happens.

To do this, we need auxiliary reference objects that reflect the geometry described by the tables (a kind of the “reference skeleton”). The simpler one represents in the 3D the H1, a1, a2 and H2 measurements:

The blue part of this object, close to the propeller axis, is still my guess – because the measurements provided in the tables start from R=400mm. (Dimensions of the blue area are copied from my actual blade models).

Another object represents the B, c measurements, as well as the calculated b1 distances in the local coordinate system of the blade airfoil. Initially I recreated them in the mesh without any twist (φ0):

I applied the twist using Hook modifiers. In each blade station I placed an Empty object. I rotated it by the φ0 angle. Then in the Edit Mode I added to the mesh object a Hook modifier for this station:

When I assigned this modifier to the corresponding Empty object and the station vertices, Blender accordingly rotated this mesh section. Repeating these steps for subsequent sections, I twisted this blade reference according to the specification.

When both auxiliary objects are ready, you can easily find the inconsistencies between the measurements from the reference table. They occur as gaps or intersecting mesh faces:

Gaps at station 400 can result from the methodology applied to this measuring process. However, differences in the more distant stations seem to be plain human errors. Their scale allows us to estimate the effective tolerance of these data.

I prepared two Blender files with the “reference sets” as in Figure ‎125‑5: one for the hollow steel blade, and another for the solid duraluminum blade.

At the beginning, it is interesting to check how the actual blade shapes, formed according to the photos in the previous post, fit these newly acquired data. This will reveal the “effective tolerance” of my photo-matching method in the case of such a complex shape. I imported blade propeller “templates” (the Blade object and NurbsPath curve – see Figure ‎124‑5 from the previous post) from my P-40 model. The scene units of these 3D references are in millimeters, while in the P-40 uses inches. Thus, for the beginning I scaled blade axis curves (NurbsPath) in the imported assemblies by 25.4. (The Blade object is the child of NurbsPath, so scaling its parent effectively scales both these objects). Figure ‎125‑6 shows the differences I encountered in these blade shapes (gray objects are my blades):

I did not compare the original twist of my blades, because it was set without any reasonable data, just to be “like in the other propellers” from that era. Instead, before this comparison I adjusted the twists of their NurbsPath curves, “lying” both blade meshes onto the green reference surface.

In general, the chord widths of my original blades are smaller than the references. I underestimated the width of the steel blade by about 10mm (along the leading edge – see Figure ‎125‑6a). It was also thicker by about 3-6mm between stations 400 and 850. In the case of the duraluminum blade, I performed a little bit better: it should be wider by about 8-9mm (along the trailing edge – see Figure ‎125‑6b). It is somewhat thicker than the steel blade and matches well the thickness measured by the Soviets.

Concluding these results: it seems that the photo-matching method is not ideal but provides better accuracy than the scale plans.

These blade meshes are twisted in a “reversible” way by the Curve Modifier, so you can easily modify their shapes by moving its vertices along their local coordinate systems. I often did this, while updating both blades. Figure ‎125‑7 shows the steel blade fitted to the reference object:

After these adjustments, I imported these blades back into my P-40 model. However, I did not import the objects, because they are in different scale (millimeters vs inches). Instead, I imported the blade mesh and the curve datablocks into the P-40 file. Then I replaced these Object Data in the corresponding blade and curve objects.

Finally, I could check the duraluminum blade, formed according to the Soviet measurements, against the reference photo. (I used the settings from the previous post – see Figure ‎124‑7):

As you can see above, they fit the photo quite well. This confirms that tables from Figure ‎125‑1a) and b) contain the measurements of the “Tomahawk”/P-40 propellers

Here you can download the Blender 4.2 files with the 3D references and the blades:

• Hollow steel blade

• Solid duraluminum blade

(In the previous post you will find the Blender file of my P-40 model, before this modification).

The classic metal propeller blade resembles a thin, twisted wing. Unfortunately, you can seldom find any detailed drawing of their geometry. Many scale plans, even those of high accuracy, often skip this detail. For example, there are accurate P-40 drawings made by Jumpei Temma. They are based on the available Curtiss blueprints and photos of restored P-40s. J. Temma drew the propellers in some of the side views, but not in the front view, so you cannot determine the blade shape.

Temma’s drawings of the “Tomahawk” propeller and spinner are based solely on the photos, because in the original P-40 documentation you can find only a few clues about this subassembly. Propellers were produced in specialized factories, usually run by another company. For aircraft designers, the propeller was just a “complete part” coming from outside. What is interesting, the key manufacturer of the aviation propellers – Hamilton Standard – still declines to reveal the geometry of their historical models (see this post).

The Curtiss company was less successful in their business: it disappeared in 1948, and the documentation of their propellers is lost. All what we have now are aircraft photos, but it is difficult to determine the accurate widths of the twisted shape blade using these pictures. The best source material that I found is an illustration from Curtiss advertising booklet from 40’s. It depicts the hollow steel propeller blade. It looks like the one used in the early, long-nose P-40s:

Thus, I made the first assumption in this section:

• I guessed that the blade from Figure ‎124‑1 is the hollow steel blade used in the P-40. I have no proof of this.

Remember, that each assumption is the potential source of errors which emerge in the future. I am making them when there is no other possibility.

The bottom picture is the most important one, because it depicts the blade “cut into pieces”, i.e., not twisted. You can also see there its cross sections! Unfortunately, the relatively low resolution of this photo does not allow for more precise measurements. Using it, I was able to create an approximated reference drawing of the “flat” (non-twisted) blade:

To facilitate forming this blade in the 3D space I also prepared the side view and the top view drawings. Some key dimensions in these views  are guessed. They are based on the photos and other illustrations from the Curtiss Electric manuals for their propellers. In particular:

• I guessed the precise location of the propeller (blade) plane on the aircraft Y axis (100” from the firewall). This station is based on the non-dimensioned side view of the propeller mechanism (its “hub”) and some faded Curtiss sketches of the spinner from the P-40 prototype.      

• I guessed the width of the gap between the blade base and the propeller axis. This gap determines the scale of the blade contour traced from the photo (see Figure ‎124‑2). I based this estimation on some drawings from the Curtiss Electric manual.         

Figure ‎124‑3 shows the 3D setup of my reference drawings:

You can find details of modeling propeller blades in this post. In similar way I created a smoothed mesh of the “flat” (non-twisted) P-40 blade, as shown in Figure ‎123‑4:

As in the case of the Dauntless model, I twisted this blade in a dynamic way. I used for this purpose a curve (actually – a straight, but twisted line running along the blade axis) and the Curve Deform modifier:

Because I had no clue about its twist, I made another assumption:

• I guessed that the twist distribution along this blade resembles other propeller blades from this period. Thus, I twisted the NurbsPath curve in the picture above as the blade from the C-47 Hamilton-Standard propeller (which was digitized in the 3D – see this post).

Then I fitted these blades into the reference photos, set up as described in this and this posts. (In the 3D, I can use these photos like scale plans):

On the right side of Figure ‎124‑6 you can see a fragment of this scene structure. (This is Blender Outliner window of my P-40 model). I placed blades, prepared as in Figure ‎124‑5, in two separate hidden collections inside Z.Instances folder. Then I inserted three instances of each of these collections around the spinner as the propeller blades. To easily modify their shape, I also created auxiliary clone of the twisting curve and the blade mesh outside these collections and placed it along one of the collection instances. Every change I apply to this clone, Blender automatically repeats in the source, hidden collection and its instances.

Then I tried to fit these blades to the reference photos. In the result:

• I found that most of the blade shape seems identical in both propeller variants (hollowed and solid). They only differ at their bases (up to 25” from the spinner axis).

• I made the tubular base of the solid blade shorter and 15% wider than the hollow blade (Figure ‎124‑7a). This is pure speculation, but this way it fits better the wider chords of the blade that occur in the next segment.

• It seems that the center plane of the steel hollow blades could be at 100” from the firewall.

• Solid aluminum blades were mounted 1.5” closer to the firewall than the steel hollow blades (Figure ‎124‑7b). Since they were heavier than the hollow blades. I suppose that such a modification improved aircraft balance. Moving the heavier propeller closer to the aircraft center of gravity (CG) helps to keep CG close to the location, where it occurred for the lighter propeller (the one equipped with the steel hollow blades).

As you can see, I used every piece of available information for recreating these propellers. The resulting blades match the photos, but I am aware that their shape is mainly based on my assumptions. Thus, their geometry still needs to be confirmed.

I am leaving this model in the state that allows for further modifications. You never know when you encounter another source of information! You can download Blender source file containing my P-40 model from Figure ‎124‑6. It is saved in the current Blender 4.2 format but represents the state of this project from 2021.

I am still working on the aircraft modeling guide. Since yesterday, its vol. 3 (of 4) is available in the web shops (645 pages, 1076 illustrations):

It teaches you how to “paint” a computer model. The course starts from the absolute basics, then in the subsequent sections we gradually enhance the initial visualization, until it resembles a real-life photo.

Here is the link to this project page. Below you can see a screenshot of two sample pages from this book:

A longer preview, including the detailed table of contents, is available in Google Books. You can also skim the free Polish edition of this guide.

“Materials and Textures” introduces the Reader to the rendering engines using in Blender: Eevee and Cycles. It shows how to create a convincing setup for a flight scene, and how to use textures for creating an impression of a war-weary aircraft.

I suppose that this guide can be also useful, as a book on its own, for all those who would like to learn “painting” 3D (hard-surface) models. Most of the techniques presented here can be also used in other programs (also in the game engines, like the Unreal Engine).

My new book on modeling historical aircraft is already available in the web shops. This is the second volume of the new (fourth) edition of the “Virtual Airplane” guide:

Here is the link to this project page. Below you can see a screenshot of two sample pages from this book:

A longer preview, including the detailed table of contents, is available in Google Books. You can also skim the free Polish edition of this guide.

“Modeling” describes how to create accurate computer model of a historical aircraft, on the example of the Curtiss P-40B fighter. It uses for this purpose free Open Source tool: Blender 3D. It addresses various typical issues, which you can encounter during this process.

I suppose that this guide can be also useful, as a book on its own, for all those who would like to learn Blender 3D (especially its “hard-surface” modeling tools).

In this post I will complete the 3D reference that I started in the previous post. Here is a link to the Blender file that contains 3D reference skeleton of the “long nose” P-40, described in the text below. It was compiled from all available blueprints.

Studying the dimmed blueprint scans, I was not able to read some horizontal ordinates placed close to the top and bottom segments of this fuselage. This created gaps in my 3D grid (Figure 121‑1a):

Fortunately, in the fuselage ordinates diagram (dwg 75-21-020) I was able to identify ordinates of two vertical planes, placed at +3” and +6” from the symmetry plane (Figure 121‑1b). This allowed me to interpolate these datapoints with curves.

Why did I try to place in this “grid” all the available datapoints? Because you can interpolate these points in different ways. For example: in the picture below the same three vertices are interpolated by two different curves:

If you have more datapoints, you can trace the resulting contour with greater precision.

Of course, in determining ultimate shapes of the interpolation curves I also used contours from the assembly blueprints:

Fitting these drawings to the datapoints can reveal additional group of wrong ordinals, which passed the previous verification. In the illustration above I adjusted the overall width and height of the blueprint fitting it to the outer vertices representing the fuselage ordinates (Figure 121‑3a). However, this contour still does not fit some of these datapoints (Figure 121‑3b). I suppose that the true contour should pass through point (3), but point (2) is located too high (by about 0.1”) to form a correct curve. In this case I decided to ignore vertex (2), because most probably this is an effect of measurement error.

Focusing on forming a single bulkhead curve does not guarantee smooth transition between the subsequent fuselage cross-sections. To avoid this class of errors, I generate their interpolations using auxiliary surface. In the few illustrations below, I am showing how I prepared the smooth contours of the tail bottom bulkheads.

I started by interpolating of the first and the last bulkhead with auxiliary surface (marked below in white):

These bulkheads form the outer edges of this “patch”. This is a subdivision surface, and its vertices are its control points – just like in the NURBS patches used in the CAD systems.

In the next step, I added a bulkhead in the middle:

Note that I marked these new edges as “sharp” (Crease = 1.0). In the effect, while the bulkhead contour is a smooth curve, perpendicular edges remain straight. In this way I can fit this surface to the stringer planes and avoid eventual problems with curvature in the planar view. (The goal of this auxiliary surface is to “produce” smooth bulkhead contours. I will deal with this two-dimensional curvature while forming the ultimate model).

In the next step, I inserted another contour between the existing ones:

In this way, by subdividing each new surface segment, you will obtain complete set of the smooth bulkheads:

You can check in the rear view if the (control) vertices of this surface form a smooth-looking mesh. (When the control surface is smooth, the resulting surface is even smoother: this ensures that there is a proper transition between the subsequent bulkhead shapes.)

Interpolating the side and top portions of the bulkheads, I prepared two other auxiliary “patches”:

Then I separated bulkhead curves from the auxiliary surfaces and “glued” them into complete contours:

Of course, these interpolated shapes are “less certain”, but more useful than the discrete “hard” datapoints. That’s why I decided to mark them in a different color: red. What’s more, I preserved the original blue polygons that represent the original ordinates. If in the future I have doubts about any part of this interpolation, they will allow me to revise the basic data.

I did not interpolate stringer lines, because radii of their curves are much greater than in the case of the bulkhead contours. Usually, for such shapes the simple “blue” polygons created from the ordinates provide enough reference.

The number of objects in this scene is growing, so I grouped them in the four basic collections:

• Blueprints – all reference images.
• Ordinates – all “blue” objects, i.e. confirmed by the explicit dimensions or ordinates.
• Interpolation – all “red” objects, i.e. smooth contours that interpolate spaces between the data points from Ordinates.
• Auxiliary – surface “patches” and other helpful stuff.

There are no engine cowling ordinates for the P-40-cu/B/C. In 2019 I found in AirCorps Library a layout (dwg L-10202), which describes the last (pre-production) variant of the XP-40. I recreated these ordinates in the 3D space:

In 2019, after detailed studies, I concluded that the X-40 radiator cover was lowered in the serial P-40s by about 1” (see this post). I assumed that the side and the upper cowling panels were the same as in this pre-production prototype. Thus, I decided that I will start by preparing an auxiliary surface for these original XP-40 ordinates:

In the next step I modified the bottom part of this shape, following the lines from my side view drawing:

As you can see, I also recreated the complex shape of the coolers inlet frame. In the AirCorps Library resources I found a XP-40 layout drawing (L-10276). Initially, I concluded that similar frame was used in the P-40-cu/B/C. However, after studying more archival photos, I decided than in the production aircraft this frame was slightly moved down (by about 0.5”), and wider.

When this auxiliary surface was ready, I copied its curves into bulkheads:

Note that I marked the modified part of the cowling (as it was in the serial P-40s) in yellow. I reserved this color for the elements based on the photos.

In the final variant of this reference, I added some additional details, like the contours of the cutouts behind pilot’s headrest:

I found their dimensions in the blueprint of the rear cockpit frames (dwg 75-21-078) and the geometry of the P-36 glass (dwg 99157, 75-21-80). I added these panels here because they are product of complex intersection of two curved surfaces.

Here you can download the *.blend file that contains complete reference skeleton of the “long nose” P-40:

In its Auxiliary collection you can also find other details, like the splitting planes of the cowling panels, gun fairings, and carburetor air scoop. I modeled their basic shapes, skipping most of the fillets. They are based on other XP-40 blueprints that from Air Corps Library.

I also placed here a simplified main landing gear. Its base (Empty) object is named S.LG Base. It is set in the “retracted” position, for which its local Y rotation is 0°. To extend this landing gear, set Y rotation of S.LG Base to +91° and rotate its leg (object S.LG Leg) around local Z axis by -96°.  

To use this model as a reference, import (File:Append) whole scene (named Reference) from this file into your project (*.blend) file. Then, in your default scene, go to Properties window, Scene tab, Scene panel, and in field Background Scene select the imported Reference scene.

This model still misses some elements, like the tail wheel assembly. In the early P-40 it resembled the P-36 tail wheel, but it was modified to fit under more streamlined doors. However, in 1941 it was modified – at least in the P-40s based in the continental U.S. Further modifications were introduced to the tail wheel leg in the “short nose” Warhawks (P-40D and later). Thus, do not use the available P-40D/E blueprints of this assembly, but recreate this detail basing on the photos.

At this moment I am working on second volume of my book about 3D modeling.  It describes building a 3D model of a WW2 aircraft on the example of the P-40B. Preparing for this work, I discovered that the original documentation of this early P-40 variant (also known as “long nose Warhawks”) is missing. On the other hand – you can find plenty of the “short nose Warhawk” blueprints (related to the P-40D later variants), as well as some P-36 drawings. I started by picking over 1000 original Curtiss blueprints and sketches related to the P-40, XP-40, and the P-36 from the vast resources of the AirCorps Library. Then I analyzed their contents, comparing them to the available historical photos. I described this process in this and following posts, written in 2019. Ultimately I traced side view of the P-40B. I also concluded that a 3D visualization of the available ordinals will be a better reference. In the previous posts I built such a reference for the SBD Dauntless. In this and the next post will I describe similar work on the fuselage of the early P-40 variants (P-40-cu, P-40B, P-40C).

I prepared an empty Blender file. For the convenience, I placed there my side view (from this post, see Figure 102-15). As for the SBD model, I assumed that 1 Blender unit = 1 in. For the main part of this fuselage, spanning from the firewall to the rudder, I used two P-36 diagrams. First of them (dwg 75-21-140) provides locations of the fuselage stiffeners at each bulkhead. There is also its modified variant (dwg 75-21-836) for the XP-40:

In fact, both layouts are identical. I can read the maximum width of the fuselage from horizontal dimensions of stringer #8, which runs along the fuselage reference line. In addition, this blueprint also provides data points for the side contour, because there were stringers #1 (upper contour) and #13 (lower contour). I suppose that the black “masks” in the XP-40 drawing correspond to the Prestone and oil radiators. In the first variant of this prototype, they were located behind the wing trailing edge in a “box” cover (like in the Hawker “Hurricane”).

There is also another diagram of the P-36 fuselage ordinates (dwg 75-21-020). However, this microfilm scan is partially unreadable:

In particular, the sketches in the lower left part of this drawing are dimmed, so I could not determine the meaning of the parameters listed in the ordinate tables.  

I began by building the vertical and horizontal plane of the fuselage. Each vertex of these meshes corresponds to a point dimensioned in the layout drawing:

At this moment I do not want to speculate about the shape in between these points, so I connected them with simple straight edges. In this way this shape represents the “hard”, dimensioned data.

For greater readability of these reference objects, I added here a few additional faces on the important contours, for example – behind the wing trailing edge. I drew them following the blueprint contours, which can be slightly distorted. Thus, they are less “confirmed” than the dimensioned datapoints. That’s why I marked them in another color. When the fuselage surface in the final model reveals a contradiction in the reference planes, these additional vertices will be the first candidates for eventual adjustments.

I decided to mark faces connecting the “hard” (dimensioned) data points in blue, while the faces created by copying the blueprint contours are in green.

On the other hand, let’s do not forget that these blueprints were drawn in the “analog era”. This means that all the explicit dimensions you can see in these sheets were ultimately measured on a “master drawing” of the aircraft geometry. Such a physical measurement always produces minor, random deviations. You can find them by looking at a high angle along any of these contours, especially along a straight segment:

The bottom contour of the P-40 fuselage in the side view forms a long, straight line (see Figure 120‑5a). However, when you look along this shape in a large zoom, you will see the deviations of its vertices (Figure 120‑5b). It seems that typical tolerance of the measurements for this aircraft was +/- 0.02”. I think that this value is possible since the typical skin thickness was about 0.03”.  However, among these datapoints you can encounter a few deviations which are greater three or four times.

In this early stage of building the 3D reference you cannot determine, if such an “outstanding” ordinate reveals a real, minor feature of the aircraft contour, or is a result of significant measurement error. Thus, I did not make any adjustments, just marking edges around such a dubious vertex as “crease”, to easily find them later.

Sometimes you can identify such an ordinate as erroneous, when you find another blueprint which provides a different dimension for the same point. When I identified that the lower part of the tables from the partially unreadable diagram 75-21-020 (Figure 120‑2) contains stringer points coordinates, it became a great help for such verification.

I created a reference “plane” for each of the fuselage stringers. Curtiss numbered them from 1 to 13, so I named accordingly each of these objects:

In addition, I found in diagram 75-21-020 a small table containing ordinates of the upper edge of the opening around the wing. I created from them another plane.

It is easier to find most of the “outstanding” data points when you build continuous faces from their ordinates, as in the illustration above. Then look along each edge of these contours. To give you impression, how many errors you can encounter in such a layout diagram, I am showing drawing 75-21-140 where I marked these identified wrong dimensions in red:

During this verification I studied again the diagram 75-21-020 (Figure 120‑2), and finally identified that its upper table contains widths and heights of the bulkheads. They are measured in the equal steps of 3” from the fuselage reference line.  Using the readable areas of these tables, I was able to recreate tail bulkheads – from #5 to #16:

I used here the equally spaced widths from the fuselage diagram. Of course, I also used other blueprints. For example – drawings 99157 and 74-21-080 provided dimensions of the “turtledeck” and the glass spanning between frames #5 and #9.

Unfortunately, ordinates that describe frames #1..#4 are not readable. What’s worse, the stringer ordinates provided only 5 data points for each of these bulkheads. I had to seek additional information among various detailed blueprints. Ultimately additional dimensions of the cockpit frame allowed me to recreate shapes of bulkheads #2 and #3, and determine the location and twist of the fuselage longeron:

As you can see, I did not find any additional dimensions of the firewall (#1), but I copied this contour from its assembly drawing. It fits the stringer points, but I marked it in green, to be fair.  Dimensions of the frames #2 and #3 revealed that their contour between stringers 7 and 9 forms an arc. The upper contour of #2A is also a combination of two arcs. Knowing this, as well as the shapes of the stringers between frames #3 and #5, I concluded that frame #4 should be a linear interpolation between their contours.

The windshield can cause troubles when its intersection with the fuselage does not look like in the photos. This happens quite often. To avoid such surprises, I decided to check this edge in this 3D reference:

I assumed that the windscreen shape was identical in the P-36 and the P-40, so the P-36 drawings (75-26-001, -012, and -026) provided me its accurate dimensions. I formed the upper part of the fuselage basing on the bulkheads #1 and #2A and the cockpit frame. Then I compared the resulting intersection edge with the archival P-40 photos. I discovered that in the XP-40 this shape of the bottom cockpit frame was “angular”, identical to the P-36, while in the P-40-cu its rear parts became somewhat smoother and moved rearward by about 0.8”. This means that in the serial P-40s they modified the shape of the fuselage between stations #2A and #3A.

Two years later, when I projected this model onto some reference photos, I discovered that:

1. The P-40 sliding canopy was ~1” shorter than in the P-36. In the effect, its 3A station which marked the base of the rear windshield frame, was 40.75” from the firewall. (In the P-36 it was 39.75”).
2. The P-40 windscreen preserved most of the original P-36 geometry, but was longer by about 0.8” (That’s I wrote in the paragraph above that it was moved by 0.8”);
3. In the P-40 the rounded corners of the gun cowling cross-section at station #2A (and correspondingly, at #3A) were higher than in the P-36. This means, that while the overall dimensions of the cross section #2A (the width at the fuselage longeron and the height), are identical in the P-36, their contours in the P-40 are different. Most probably they modified them to better accommodate the pair of the M2 guns, mounted in the P-40.  

All these observations contributed to the different shape of gun cowling-windscreen intersection edge which I observed in the photos. I recreated all these findings in this 3D reference, creating the P-40 gun cowling and the cockpit as gray, surface objects.

In the P-40B/C Curtiss introduced another modification to the windscreen frame, enlarging the inspection doors above the fuselage guns:

However, it did not alter the fuselage cross-sections, so I decided to skip this variant here. Because of this overlapped gun door, the windscreen frame in the P-40B/C is a quite complex shape. I think that it will be easier to form it starting with the previous, simpler variant of the P-40-cu, then apply the later modification.

I decided to upload the Blender file in which I reproduced in the 3D space the original ordinates of the SBD fuselage and wing. (I described creation of this 3D reference in my previous posts). I think that in this form they can be useful for other modelers, who would like to recreate the geometry of this aircraft. Here is the link to the *.blend file (102MB) that contains the model presented below:

The fuselage ordinates are organized into horizontal “water lines” (blue), vertical “buttock lines” (green) and resulting sections (red). Each vertex of these polygons corresponds to an original ordinate (data point). For simplicity, I connected these vertices using straight edges. (You can find more details about these “reference polygons” in this post).

As you can see, there are also original blueprints in this scene. In fact, they are the only reason of the large size of the uploaded *.blend file. In the initial view most of them is hidden because they would obscure all other objects. For example: I clipped from various assembly drawings silhouettes of the assembly frames. Each of these images is assigned to the corresponding section.

To manage this complex structure, I organized it into two basic collections named Wing and Fuselage:

Each of these collections contains a sub-collection named Blueprints and a sub-collection named Ordinates. Blueprints contains clips (raster images) of the original Douglas drawings. Ordinates contains the reference meshes (planes) recreated from the numerical ordinates provided in the Douglas blueprints.

Note the alphanumerical prefixes in the collection names (like “#5.A2a..”). I added them just to ensure that each name is unique. (This is a requirement in Blender.)

You can turn on/off visibility of these collections, as well as the individual visibility of their objects. For example: I manually turned off visibility of most of the reference images. I am turning them on when I need them.

The internal structures of the Blueprints and Ordinates collections differ from each other. In the case of the wing, both are split into three sections: center wing, outer wing, and wing tip. In the case of the fuselage, Blueprints contains just a sub-collection for the bulkhead blueprints (Frames), because there were so many of them. Fuselage ordinates (i.e. polygons) are organized into separate collections for the Buttock lines and the Water lines. There is another collection: Stiffeners, but its data are less reliable, because they were provided as single values per each fuselage station. For the stiffeners #0, #1, #2, #12, #13, #14, #15, which are closer to the fuselage centerline, ordinate tables provided their widths. For the other stiffeners (#3 … #11) ordinate tables provided their heights from the fuselage centerline. It seems that Douglas engineers “traced” them by projecting onto the surface described by the buttock lines and the water lines.

In the Sections collection I placed cross-sections of the fuselage buttock- and water- lines. The only additional information there are the arcs between these data points. (For example – in the fillets that span between the fuselage and the wing, or between the fin and the stabilizer.) I recreated them using the radii provided by Douglas (in the blueprint with the fuselage ordinates). These radii were not complete, but they are better than nothing. It seems that the SBD designers used a fixed 3” fillet radius where they could.

You can easily identify these assumed (non-confirmed) data points of the fuselage sections, because they do not belong to any horizontal or vertical line:

These horizontal and vertical lines are the traces of the corresponding buttock planes and water planes. I left them in the resulting mesh as additional, disconnected edges.

In some water- and buttock- planes I also added a few additional vertices, to match better the eventual fuselage surface. (This is a purely aesthetic purpose.) They are non-confirmed by any numerical ordinate. For easy identification, I colored the additional faces created by such a vertex in brown:

The last Fuselage sub-collection, named Interpolation, holds my approximation of these ordinates. First of its sub-collections, named Surfaces, contains  smooth surfaces that I spanned over the buttocks- and water- lines:

I described details of these surfaces in the previous post. They are something between a pure reference object and an initial attempt to forming the fuselage with smooth subdivision surfaces. (Shaping these contours, I learned about the minimum number of the control polygons that are needed to fit all available data points). You can also see there a windscreen “wireframe”. I built it using the dimensions from the cockpit assembly drawings. I needed these lines for reconstructing the shape of the guns cowling, which was not described by the original ordinates.

Two other Interpolation sub-collections, named Frames and Stiffeners, contain smooth interpolation of the fuselage bulkheads and longerons:

In addition, I also modeled the oblique parts of the bulkheads at station #4 (object: R1.Frame#04o), #5 (R1.Frame#05u) and #7 (R1.Frame#07b):

In the uploaded file their visibility is initially turned off.

Ultimately, this file also contains some reference photos. Each of them is assigned to an auxiliary camera which projects this model onto this photo. To easily switch between these projections, download this add-on and install it in Blender. It adds additional Cameras tab to the 3D View property pane (the one which you open using the [N] key). Use its contents to switch between available photos:

You can find more details about this add-on at the end of my tutorial on photo-matching (see the description around its Figure 104-26).

Playing with these photos, on three of them I observed a difference in the upper part of the windscreen contour:

While the bulkhead and stiffener lines (thin black in the picture above) perfectly match the photo, there is a difference in the windscreen heights. This requires further investigation, because I formed this 3D shape according to the explicit dimensions from the original cockpit canopy blueprints. Of course, I could make an error while creating these lines.

I observed similar (but not identical!) differences in the photos of another SBD-5, from the Pacific Aviation Museum Pearl Harbor:

The resolution of this photo is lower than the previous one. However, it is still enough to reveal this “offset”. At this moment I cannot exclude the possibility that these minor differences were created by the renovation teams. (It seems the least probable explanation, especially in the case of the Pacific Aviation Museum).

For over ten years Hugh Thomson has published marvelous posts in his blog about the historical aircraft. Just look there to see the P-51 Mustang, F6F Hellcat, F4F Wildcat and B-25 Mitchell CAD models and – what is sometimes even more important – compiled datasheets of their ordinates. The true, accurate geometrical data are usually dispersed and difficult to reconcile in the thousand sheets of the faded out, barely readable original blueprints. Hugh studied them all and is providing this information in the easy-to-use form. If you need such data on any of these aircraft – visit his page and choose any of these packages, or just make there a donation, to support his future projects!

Below I am enclosing some screenshots of his research work:

Note that Hugh is also providing complete sets of the original blueprints scans. This is much better option than buying them from the source that I previously recommended (plans.aero – in this post). The big advantage is that by sending an e-mail to Hugh you are not contacting an impersonal Internet portal. Here is a real mechanical engineer, a specialist, who worked with these scans and knows all “pros and cons” of each package. Before buying any of these aircraft blueprints you can ask Hugh about its details, blueprint quality, image resolution. Highly recommended!

In the previous post I used ordinals from the newly found fuselage geometry diagram for creating a set of the 3D reference planes:

In this post I will span a smooth subdivision surface between these points. I think that such an interpolation will provide a more accurate reference than the longerons (stiffeners), which I previously shaped in this post (see there Figure 112-07).

I compared my previous approximation of the fuselage shape, based on the partial data from the NASM microfilm, with these ordinates. In general, it seems that it was quite accurate:

The wing fillet fits well these ordinates – its shape requires just some minor adjustments. On the other hand, I can see that the radius of the upper parts of the tail bulkheads was somewhat smaller. At least I was right, assuming that this radius was constant along the rear gun doors. In this way these doors could be formed as a part of the cylindrical surface, which simplified their production.

Ordinates from this SDASM blueprint confirmed many of other assumptions that I made basing on the partial NASM blueprints (see my first two posts on the fuselage geometry):

Note the flattened cross-section of the wing root fillet. This diagram confirms my hypothesis about this shape, based on the shape of its trailing edge in the top view (see this post). It also confirms another assumption: that in the rear view all the fuselage stiffeners (I called them “longerons”) run along straight lines, spanning radially from the fuselage center. In the tail area, these lines are equally spaced: 15° from each other. In the mid-fuselage some of them are bent upward.

When I looked at the forward part of the fuselage described by the Douglas geometry diagram, I realized that there is something wrong with the upper contours of frames 1 and 2:

While most of the frame 1 data points perfectly fitted the firewall assembly drawing, they missed the “bulged” covers around the fuselage guns. Fortunately, I was able to recreate this cowling using dimensions from the windscreen and firewall assembly drawings.

I think that this diagram was based on the original Northrop XBT-2 prototype drawings. As you can see below, the upper cowling between frame 1 and frame 2 looks like in the geometry diagram:

XBT-2 was equipped with a single forward-firing gun, mounted on the right side, in the front of the pilot. Thus, left contours of its frame 1 and frame 2 could match the elliptic shape, depicted in this diagram. I suppose that the geometry of all other XBT-2 fuselage frames (3 … 17) match their counterparts in the serial SBDs.

Illustration below shows the smooth surfaces, spanned over the reference polygons. In this case, I corrected the shape of the wing fillet surfaces (blue and red), extending them up to frame 13. Then I added new surface (gray) which covers the main portions of the fuselage. Behind the cockpit, I fitted its shape to the cylinder. Upper parts of this cylinder cross sections fit the corresponding ordinal points of the fuselage frames:

To make sure that this “skin” passes through the original geometry, I placed it little below the ordinal points. In the effect, the vertices of the reference polygons minimally protrude from this surface – by about 0.01”. This is well within the range of eventual errors in locations of these ordinal points, and below the thickness of the real fuselage skin (0.03”). In this way I was able to visually check if the modeled surface fits all ordinal points.

On the other hand, the geometry of the WW2 aircraft was always given “as for the skeleton”, i.e. did not take into account the skin thickness.

When I compared the resulted shape with the fuselage assembly blueprint, I saw that its upper contour precisely follows the ordinates. There were some minor differences along the bottom contour plotted on this drawing:

These minor differences are OK, since these lines on such an assembly drawing are of least importance. In this blueprint, the key information are the referenced part numbers.

However, some months ago, when I did not have these explicit ordinates, I concluded that the upper fuselage contour was 0.3” higher than on this blueprint (see this post, figures 113-7 to 113-9). It looks like that on this high-resolution photo, which I matched  with my model:

Because the explicit dimensions did not confirm these findings, I verified this hypothesis using matched photos of another restored SBD-5:

In both aircraft we can see identical difference in the dorsal fillet shape, but the fuselage, shaped according to the ordinals, perfectly fits the second picture. There is no visual difference, especially as significant as 0.3”. Thus – this higher upper contour is an individual feature of the restored SBD-5 from the first photo. Most probably they inaccurately rebuilt its tail section.

When you are looking into something for too long (as I did in the case of this fuselage) you can sometimes “find” a non-existing feature! In such a case, the explicit dimensions, as these ordinals, are invaluable.

On the other hand, I suppose that these photos depict the true shape of the dorsal fillet. (Unfortunately, its ordinals were provided in a separate blueprint, which is still missing.)

This February I found among the SDASM resources a diagram (dwg no 5060837), which describes the geometry of the SBD fuselage. This is the key piece of the information that was missing in the NASM microfilms I used before. Below you can see these lines:

The original drawing is slightly distorted. I was able to stretch its upper and lower portions, so in the central part its rectangular “grid” fits the blue guide lines drawn in Inkscape. However, this is a non-linear deformation, so it still occurs along the edges of this image. (In the illustration above, I marked these distorted areas in pink.)

The subsequent fuselage frames are placed at following stations:

Fortunately, fuselage diagram contains not only these distorted lines, but also tables of their numerical ordinates. They are provided for equally spaced horizontal and vertical “grid lines”, as in the illustration below:

The diagram provides two tables. One of them lists at each frame the fuselage widths along the horizontal lines (“waterlines”). The other provides heights of the upper and lower contour, measured along the vertical lines (“buttocks lines”). For some frames, like Frame 9, the table provides more than two heights, as show in the illustration above.

I used these numerical data for building corresponding “contour planes” in Blender 3D space:

Each of these planes is a polygon. Each vertex of these polygons corresponds to a single ordinate. These vertices are connected with straight edges. (On this stage, I did not want to interpolate them with curves.)

Then I used the same data points for creating section contours:

They are also simple polygons: vertices connected by straight edges. Because I generated them from the cross-sections of the vertical and horizontal planes, you can see on each of them the characteristic “grid” pattern.

Building these shapes, I found some obviously wrong points in the waterlines. In the table below I marked them in red:

Fortunately, the table of the buttocks ordinates is less erroneous. Just some data points are shifted to a wrong column. (In the figure below, I marked these values in yellow):

There are also others, less visible inaccuracies. In that times all these ordinates were measured from large drawings (some of them were in the 1:1 scale). Still, you cannot avoid minor measurement errors in such a manual drawing.

Once I placed these values in the 3D space, I examined resulting lines, looking for irregularities. For example, I found a suspicious point at station 7, on the cockpit frame:

The vertices from the previous frames (1..6) formed around this cockpit edge a polyline which you could extrapolate with a gentle curve. These data points were somewhat dispersed, but no more than by 0.02”. However, the vertex at frame 7 lies about 0.1” from this extrapolated curve. Was it a measurement error, or a real feature of this shape? To determine this, I checked the nearest waterlines (at +16”) and buttocks lines (at 16”). I did not find similar deviation there, thus concluded that this is just an error, and adjusted this outstanding vertex.

However, when I noticed a recession which repeats in the three subsequent waterlines – I concluded that this is a real feature:

I suspect that this is a “side-effect” of the large fillet between the wing and the fuselage.

In general, I assumed that the error range for these ordinates was about 0.05”. There are just a few larger deviations, as the one at the cockpit edge.

There are also differences between the data points plotted according to the numerical ordinates and the fuselage lines depicted near these tables. In the illustration below the plotted lines are in black, while the reference polygons (created according to the numerical data) are in orange:

I suppose that these inaccuracies are mainly caused by the irregular distortions of the scanned blueprint. On the other hand, drawings in this diagram are just illustrations for the numerical ordinates. Thus, you should not treat these black lines as an accurate reference.