NAA P-51D Mustang: Wing Ordinate Rev

NAA P-51D & B/C Mustang: Wing Ordinate Major Update:

Thanks to Roland Hallam, I am now in receipt of new verifiable information that has prompted a return to the P51 project and a major update to the wing ordinate data sheets.

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Many of the blanks have now been filled in and new additional information added. The above image is a snapshot of the work in progress. The groups highlighted in blue are checked verified dimensions, the red values are those that have changed and those areas remaining in white have prompted an interesting conclusion. Up until now, it was presumed that the wing profiles for the P51D and P51C were the same with the exception of the wing root, however, closer inspection would now suggest that a few rib locations are also slightly different which requires further investigation.

I am still working through the new information and dissecting what is relevant to the P-51D and the P-51B/C variants. This will probably take me a while to evaluate but I am confident that this will result in the most comprehensive dataset yet compiled for the P-51 wings.

I had not expected to return to the P51 project at this time but I’m sure you will agree this is an exciting development.

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Technote: Icosahedron Edge Calc

Technote: Icosahedron Edge Calculation:

Geodesic geometry is rather interesting and occasionally quite challenging. I have recently been involved in a project to explore construction options for a structure based on an Icosahedron form. Although the basic geometry was created using Inventor I was curious about the underlying mathematical formulae pertaining to this type of geometry. I also like to be able to verify key dimensions in the 3d model by separate calculation.

One site I would recommend for calculating this stuff is Rechneronline which provides various options for calculating based on known criteria, an example of which I have shown below.

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The formula provided are comprehensive but lacking specifically the formula I was looking for to calculate the edge length for a given radius. The fourth formula in the list does include the value (a) which is the Edge Length and therefore can be transposed to determine the value we need.

Here I have rewritten the fourth formula with the value (a) shown as (L) for clarity.

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To determine the value (L) the transposed formula would be thus:

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This is a small snippet of information that I hope may be of some use for anyone interested in Geodesic geometry.  I should note that the 4 is a multiplication of the sum of the parenthesis and not a power to 4 superscript.

To use this in Inventor the formula can be entered as follows in the parameter dialogue box as a user parameter called “EdgeL”:

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The resulting Model value verifies the “d112” dimension from the 3d model.

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Excel Spreadsheet Technote:

1. Use names in lieu of cell addresses

Consider the ideal gas law (Wikipedia) calculation in the Excel spreadsheet in Figure 1.

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Figure 1. For easy readability, this ideal gas law calculation has labels in the left column, values in the center column, and units in the right column.

Contrast the following formulas for calculating the value in cell C6:

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Although this is a simple example, the advantage of the formula on the right is evident. In order to reverse-­engineer formulas that use cell addresses, such as the one on the left, you would have to trace back the source of each quantity. The formula on the right uses cell names that relate to the variable names from the familiar algebraic ideal gas equation. The style of the spreadsheet layout also improves read­ability. In Figure 1, the labels in column B are the same as the names for the cells in column C.

There are three common ways to create names for cells. A convenient method is to select the cell, and type the name into the Name Box field above the column A label:

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You can also transfer the label from an adjacent cell onto the cell of interest using Create from Selection in the Defined Names group on the Formula tab of the Ribbon (Figure 2). In fact, more than one label can be transferred with a single command.

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Figure 2. Create names for cells using the Create from Selection command.

 Use the Name Manager in the same Defined Names group to create, edit, and delete names. Cell names generally have global scope in the workbook, but it is possible, using the Name Manager, to create names that have scope only in the worksheet where they are created.

Note that certain names are not allowed. First, you cannot create a name that is the same as a cell address. Given the size of the modern worksheet (the Excel spreadsheet has 214= 16,384 columns and 220 = 1,048,576 rows — a total of 234 cells), with columns out to XFD, it is easy to confuse a name with a cell address. Second, you cannot use the letters R or C as names or those letters followed by any digits. This restriction harkens back to the R-C method of cell addressing (i.e., row-column), which is rarely used today.

The following shows an example of practical formulae using named cells.

2. Set up calculations in their natural sequence and targeting methods.

It has been said before many times to start at the beginning and finish at the end. For most engineering problems, there is a natural sequence that starts with basic data and proceeds step-by-step to a final result. However, in many calculations, you may need to find one or more starting values that yield a desired final result, or a target value (Figure 3). The target may be a specific value, or it could be the minimum or maximum of a function, such as cost or profitability. The calculation may have more than one input cell, and there may be constraints on various elements of the calculation.

Figure Template Standard

Figure 3. Targeting methods, such as Goal Seek or Solver, can help you determine the input value that yields a desired output or target value.

For one-time solutions of these targeting problems, you can often simply adjust the input value by trial-and-error and meet the target after only a few tries. Excel offers two tools that automate this procedure: Goal Seek and Solver. (The Solver is an add-in provided by Frontline Systems. For information and guidance on using the Solver, see www.solver.com.)

Excel’s Goal Seek is only able to solve target value problems. It is a black-box tool that does not give the user options or control over its numerical procedure. For example, we want to determine the liquid depth in a 4m-diameter spherical tank that corresponds to a volume of 10 m3. The formula is:

08-B2B_Spreadsheets_Eq_1

where V is the volume, h is the liquid depth in the tank, and Rd is the radius of the tank. We set up a calculation on the spreadsheet based on a test value of 2 m for the depth (Figure 4a-b).

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Figure 4. The total volume of a liquid in a tank is calculated for an arbitrary liquid height of 2 m (a) by the formulas shown in (b). Use Goal Seek to set the volume equal to 10 m3 by changing cell h (c) to find the depth corresponding to a 10-m3 volume (d).

Invoke Goal Seek from the What-If Analysis drop-down list in the Data Tools group of the Data tab of the Ribbon. Complete its fields, as shown in Figure 4c, by setting cell V equal to 10 m3 by changing cell h. Upon clicking the OK button and accepting the result, we have the solution that h = 1.45 m (Figure 4d).
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Hoppers: Surface Model for Mass Containment

Hoppers: Surface Modelling for Mass Containment:

Although not directly associated with aircraft design there are inherent modelling techniques equally applicable to many aspects of aviation. The techniques relate to surface modelling for the containment of a known mass or volume. In each case, the criterion is the specified volume or mass that ultimately defines the size and shape of the container.

hopper-1

This particular hopper is for a Transfer car used to feed Steel Plant Coke Ovens with coal. The development of this hopper combines surface and solid objects in a single multi-part model that is configurable via a dialogue populated wth the key parameters. Surface modelling can be used for various purposes; some of which I have covered in previous articles for the creation of sheet metal flanges, trimming solids and providing a boundary for extrusion or as a containment for a solid component; as I have used here.

hopper-master-01

This type of hopper is fed from an overhead bunker and releases the fill material through an aperture in the base. The mass volume is modelled according to industry specifications that define the slope of the poured coal defined by the size of the top bunker opening.

The surface represents the containment boundary which has zero volume and zero mass therefore by definition will ensure that the only properties recorded for mass and volume in the 3d model relate only to the fill material. The image above shows some of the key parameters used to model this hopper as a part file with an ilogic form to make it easier to adjust the parameters to suit the project design.

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The gray values for the Coal Volume and the Centre of Gravity are the results calculated from the physical dimensions of the coal mass and the containing surface model. Once the correct dimensional and mass properties are determined the surface objects are extrapolated using the “Make Component” command in Inventor which creates a separate derived part file and also (optional) includes the part file in an assembly placed at the original coordinates. In the surface part file we simply thicken the surface to generate the solid plate material that will form the structural body of the finished hopper.

hopmaster01assemblya

This is a very basic introduction to using surfaces where the mass or volume of a fill material is the critical component. On some forums, similar questions have been asked for complete hoppers where programmed solutions are offered to subtract all the structural objects to derive the fill mass and volume. By using surfaces with zero mass and volume to contain the fill there is no need for any programming solutions. There are a few ilogic basic routines included in this example for formula calculations and shifting the location of the bunker output. Another example just for reference is the casing for a screwfeeder:

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Surfaces are extraordinarily versatile with many applications, only some of which have been mentioned in this blog. For this example, we could extend the technique to modelling fuel tanks, hydraulics and oil tanks where the volume and mass are critical.

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Sopwith Pup:Wing Brackets

SopwithPup: Wing Brackets

This was not meant to have been a study in its own right, but out of curiosity I couldn’t help but wonder if there was enough information to actually build an accurate 3D model.

I was also curious why I had received a number of help request emails from my friend about this particular aircraft…so I decided to have a closer look. His latest query was regarding brackets similar to the one I mentioned in my previous post but specifically the centre section connecting brackets to the wings.

The left bracket belongs to the centre section and the right bracket is the connecting bracket for the wing that slots into the centre section bracket.

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The bracket dimensions are such that the centre bracket sits proud off the centre spar whilst the wing bracket is embedded in the wing spar, so technically they should just fit into one another without too much problem!! That’s the theory but the reality is it doesn’t quite align with expectations.

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This image shows the actual clear dimensions within the top and bottom rib flanges which replicate the perimeter dimensions of the wooden centre spar. In order for the centre section bracket to connect to the spar we would have to notch the top and bottom rib flanges to get it to fit. The horizontal dimension can vary (highlighted) but we will be restricted by the vertical dimension. I can’t imagine why anyone would want to notch the top and bottom flanges as this diminishes its strength. Plus there’s another issue with this…

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This preliminary model shows the problem where the centre spar is actually set back one inch to facilitate the incoming connecting bracket from the main wing. Ideally, we need to fully assemble the centre section and have it fitted to the aircraft and aligned prior to fitting the wings, but how can this be done if we can’t screw the rib flanges to the spar? I think in this instance I would shape the wooden spars in such a manner as to facilitate fitting of the flanges and mating with the wing spars.

I have done some research on this and it appears to be a known issue with some clever blokes just redesigning the connectors to make it work better or tapering the wing spar to good effect as shown below.

sdasmpup

It looks as though the wing spar is tapered with a smaller bracket sized to fit within the centre bracket. That would work and likely an improvement implemented in the workshop. A very rough preliminary study could look something like this…

…it does need a lot more work but I don’t have a lot of time to develop it further right now!

The design in many respects seems a little rough and ready, but we have to remember in those days they were under a huge amount of pressure to get these aircraft built and get them into the field. The life expectancy of these aircraft was only six weeks so replacements had to be shipped out in rather a quick time.

No disrespect either to Tom Sopwith and his engineers, these things actually flew rather well regardless of the vagaries of the design and what may seem to be annoyances to us may well be things they would naturally deal with in the workshop without any hassle.

It is very tempting to continue developing the Sopwith Pup but to do so efficiently would require setting out the basic geometry for the entire aircraft, identifying the anomalies and determining suitable resolutions as close as possible to the original design intent. I’m not sure I have the time nor the inclination to do so.

This has been a welcome distraction from the P-39 Airacobra project and will likely feature in a few more posts as I will surely continue to receive help requests from my good friend.

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Sopwith Pup: Technote

Sopwith Pup: Spar Clip Technote

The Sopwith Pup is a single seater biplane built by the Sopwith Aviation Company, another aircraft in my archive, though not one that I have done much work on. This is just a quick technote; so not a new project; my priority still lies with the P-39 Airacobra.

I received an email from a close friend and he asked if I could help him out with this model for the main spar clip, item number 1393-1 from the Sopwith drawings. The area in question was the cable lug at the base of this clip, which comprises 2 parts.

The problem related to matching the profile of the top part to the profile of the lower part, without extensive or complex modelling. For the lower part, I decided to use the sheet metal features to create this as a multi-body part which I would then use as a template to profile the upper section that is essentially an extension of the main model.

What he was trying to do was project a sketch from the each face of the lower part, extrude each sketch and then fit a bend to connect the two extrusions. He reckoned this was more complicated than it should be and asked me if there was better way of doing this.

He was actually not that far from achieving a simpler solution, he just needed to adapt the process a little bit.

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In a previous article for the P-39 cabin glass I discussed the merits of selecting the solid surfaces as a means to modelling the jogged edges. I have used a similar technique here for developing the upper part of the lug.

Simply by selecting the top surfaces of the lower part as shown above; we then apply a thickness to this selection and opt to merge with the upper part as shown. There we have it; an exact match and fit between lower and upper lug parts in one step!.

It looks simple and often the best solution is, but occasionally it is easy to overlook the fact that we can manipulate the surfaces of a single solid model to create new separate parts without too much effort.

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Squaring the Edge:

The Sopwith drawings for this part and many other similar parts are a little misleading given that they show the edges of these components as beveled. This is normally not good practice, particularly when metal meets timber. Ideally we need to square the edges to negate this problem and to facilitate the cutting of the developed sheet metal pattern.

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These brackets are an awkward shape which requires some careful planning to ensure that the model is correct and can be manufactured. So to achieve this I occasionally use surfaces to set-out the basic cut profile shape and then thicken.

Thickening a surface model is actually a good way of working due to the thickness being applied normal (perpendicular) to the surfaces, thus by definition achieving a good square edge to the developed pattern.

As you can see in the image on the right the edges are square and easy to cut.

The other way of doing this is using the cut option feature from the sheet metal command.

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By selecting the “Cut Normal” option in the dialogue this will ensure that each of the edges from this extrusion will be square to the surface when flattened.

Whilst we are on this subject; the weld seam at the top of this bracket is something I would consider improving by having a thin continuous metal strip either side of the seam instead of 3 smaller widths (top image) which may distort the metal, something like this (A):

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Notice I have tidied up the bend at (B)…this gives a much cleaner profile when the draft angle is quite small. I should note that I don’t normally take liberties wth the manufacturer’s details, but occasionally exploring options to see how things could be improved can be quite an interesting exercise.

I should note that it is normally good practice to state on the 2D manufacturing drawing a “Break Edge” minimum size anyway for all edges even when square cut.

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Bell P-39: Progress Update

Bell P-39: Progress Update; Comparison

Progress to date has focussed on the main inner fuselage development with additional modelling to the top cockpit glass.

Just for comparison and to give you some idea of scale and context I thought it may be prudent to bring together a photograph of the P-39 and the CAD model, that are roughly shown from the same viewpoint.

p-39_airacobra_2006-06-15

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Ordinate Observations:

I mentioned before that we don’t have an ordinate plan for the P-39 as the main ordinates are incorporated within the Bell part drawings themselves. One of the key objectives for this project is to create an ordinate plan for the main fuselage to ensure that everything matches perfectly. Typically for all manufacturers of this era, the Bell drawings are accurate to 1/64 inch (0.4mm) in some cases but more generally dimensioned to only 2 decimal places of an inch that occasionally results in some minor alignment issues.

An example is as follows:

The upper structure for the cabin has ordinates setout for defining the contour of the main structure which overlaps the fuselage outrigger as shown. The fuselage outrigger profile does not quite match either the dimension nor the curvature in this instance.

If we look at the ordinates for each part we can see the difference is exceptionally small although well within the manufacturing tolerances.

WL (waterline) 12: Cabin noted as 16.98in  –  Fuselage noted as 17.006in

WL (waterline) 16: Cabin noted as 16.26in  –  Fuselage noted as 16.286in

The difference is only 0.026in which equates to 0.6mm. Admittedly some ordinates are given to the outside of the skin, others are not and it’s tempting to suspect that the variation is due to this. The skin though is 0.04in almost twice the difference.

Working with CAD these variations are quite obvious and ideally need to be sorted otherwise we end up with all sorts of interferences with adjoining components. This makes it rather interesting and challenging in order to derive a satisfactory model.

In this example the curvature analysis shows this point close to being negative curvature in the left image based on the ordinate value of 12.88in. We know that this dimension is a decimal equivalent of 12 7/8 inches which at 3 decimal places gives us 12.875.

Changing the value thus to 12.875in smoothes the curve in line with expectations.

The majority of the Bell P-39 drawing dimensions are in fact very accurate, with the first example above being the exception rather the rule. This is an update of the ordinate developments for the fuselage which is derived from multiple part drawings.

p-39-airacobra-fuselage-ordinates

 

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