Floft: FIGURE 1

Lofting Fuselages The Easy WayWhen I got my first computer in 1980,

one of my maiden projects was to writea lofting program. It has evolved overthe past ten years into FLOFT. This ar-ticle describes what FLOFT does andhow it was used to help develop thefuselage of a particular airplane ...namely, John Roncz's DLR.

To loft a body is to define its shape.I believe the term dates from the dayswhen boats were constructed on themain floor of a building, and full-sizepatterns for their frames were laid outin a spacious loft overhead. The chal-lenge of lofting a boat, or any otherstreamlined body, is to develop cross-sections that blend properly into oneanother. This is most easily done if thecurves used are all members of thesame mathematical family.

Various geometrical and computa-tional procedures have been used toproduce such families of curves; theclassical one in the aircraft industry,which was first applied in a thoroughgo-ing way in the design of the P-51, is themethod of second-degree conic curves.Although it has now been partlysupplanted by other techniques in themanufacture of large airplanes, thismethod is still completely appropriate tosmall airplanes. Among its advantagesare its ease of use and the fact that thecurves it generates are always (like theP-51's) pretty to look at.

Until the advent of digital computers,loftsmen used straightedges to lay outswarms of lines - based on a geometri-cal demonstration by the Frenchphilosopher Pascal - which eventuallyyielded strings of intersections lyingalong the desired curves. With com-puters it's all much simpler and, ofcourse, faster; you tell the computer afew parameters for a curve, and it im-mediately spits out either a picture of it,a list of coordinates along it, or a plot

By PETER GARRISON1613 Altivo Way

Los Angeles, CA 90026

CHIMERAFS 100.000Scale I1 - 5.00*6/17/90

FIGURE 2

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FIGURE 3

Having drawn these lines (we will bechanging them as we go, so they don'thave to be precise just yet), we nowhave to convert them into conic curves.Unless we're designing something ofvery simple shape, like a blimp or a BD-5, it's unlikely that a single conic will dofor a given line; we'll have to break upeach moldline into two or three or moresegments, each of which we can closelyapproximate with a conic.

There are lots of ways to go aboutbreaking up a curve into segments,since conies can have lots of shapes;for starters, however, the easiest thingto do is to put breaks wherever thecurve is flattest. For example, look atthe side view of DLR in Figure 1. The

BW has an obvious break at around FS185 where the curve changes from con-vex to concave; there the curve ismomentarily perfectly flat. Another nat-ural break seems to occur somewherealong the bottom of the cabin aroundFS 100.

We now draw tangents to themoldline at each break point. For eachcurve segment, the tangents make aframe; the coordinates of the fore end,the aft end, and the intersection of twotangents, together with a fourth valuecalled the K factor, fully describe theconic curve for the segment.

The K factor is a number, convention-ally between .5 and 1, that describeshow closely the conic hugs the frame.

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The first step in lofting a body by anysystem is to draw a picture of it. Thiscan be done with a CAD program(which FLOFT isn't) or with paper andpencil. John Roncz uses the formermedium, I use the latter. As anyone whohas even toyed with airplane designknows, the first stage of design is thatof laying out the locations and sizes ofpowerplant and people, and then en-closing them in a pleasing-looking en-velope (and preferably one free oftroublesome drag).

We need four main lines, calledmoldlines: the Top Waterline (TW),Waist Waterline (WW), Bottom Water-line (BW), and Maximum Buttline (MB).(In lofting parlance, waterlines are verti-cal dimensions, stations are lengthwisedimensions, and buttlines or buttocklines are widthwise dimensions.) TWand BW are what you see in a profileview of the airplane. MB is what yousee on both sides (FLOFT assumesairplanes are bilaterally symmetrical) ina top view. WW is the waterline (that is,the height in relation to some horizontalreference plane) of the MB - the pointat which the fuselage is widest; it mayjust be a horizontal line down the middleof the airplane, or it may have a morecomplicated shape.

10?T DATA SUItlflRY

File MM: DIDLast revision: 4/19(90

Sott01 naterline

Scents: 4

Fore end 57.0000,-6.0000A f t end 56.0000,-17.6000Corner 40.2000,-H.2000I (actor 0.7000

56.0000.-I7.400096.0000, -21.380048.4400,-20.2600

0.7500

It.0000,-21.3800195.0000,-14.5600149.0000,-23.5000

0.8000

185.0000,-14.5600293.8280,-5.2500222.5000,-5.2300

0.7500

Haist laterline

Shunts: 2

Fore endAft endCorner

K factor

37.0000,-3.500048.0000,0.000040.1000,0.0000

0.7500

48.0000,0.0000293.8280,0.0000

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lop naterhne

Fore end 37.0000,0.0000Aft end 91.5000,10.7500Corner 42.0000,10.7500

1 factor 0.7500

91.5000.10.7500180.0000,18.5000113.0000.40.4000

0.7500

180.0000,18.5000293.8280,4.2500210.0000.8.5000

0.7500

FIGURE 5

54 SEPTEMBER 1990

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A K factor of 1 means that the curvecoincides exactly with the frame. A Kfactor of .5 means that the curve is astraight line joining the ends of theframe. A K factor of .707, when appliedto a square frame, produces a circle.Figure 2 illustrates the significance ofthe K factor: it is the fraction of thelength of a diagonal intersecting thecurve that lies on the "center" side ofthe curve.

We use a little program called SEEKKto get the K factor for each segment ofeach moldline. SEEKK asks for thecoordinates of the frame and of up toten points that lie along the line we aretrying to match - that is, the line we drewin the first place. It then reports the Kfactor that best approximates the givencurve, together with a figure of merit in-dicating how good the match is. If it isn'tup around .96 or better (1.00 is a perfectfit) we need to consider relocating oursegment breaks.

Figure 3 is an example of SEEKK inaction, making a first cut at the first seg-ment of the bottom waterline for DLR.The dimensions are simply scaled fromthe drawing, which needs to be bigenough - 1/10 scale is good - to allowyou to pick off measurements withreasonable accuracy. Since the tan-gents are straight lines across the seg-ment breaks, we use two other supportutilities, POLATE and XING, to findexact locations for third points on frame

lines, given any two.We got through this same operation

for each of the segments of each of thefour moldlines, each time noting downthe coordinates of the segment endsand of the frame's "corner", as well asthe K factor for that segment.

Now we have roughly defined theside and top views of the body; butwhat will the cross-sections look like?Square? Elliptical? Squarish but roundedat the corners, like a TV screen?

FLOFT will build cross-sections in thesame way we "built" each moldline seg-ment; that is, by generating curves fromsome coordinates and a K factor. In thecase of cross-sections, FLOFT as-sumes them to be inscribed in a rec-tangle, with top and bottom halves di-vided at the WW. The rectangle's widthat any FS is twice the MB, and its heightis equal to the difference between theTW and the BS. The cross-section inFigure 2 is typical. The top half of thecurve has a K factor of .77 and the bot-tom half one of .80.

The top and bottom K factors of fuse-lage cross-sections will vary along thebody. For instance, one might be .707(round) right behind a spinner, then goto .8 on the top and .85 on the bottomfor headroom and footroom in a two-seat cabin, and then return to, say, .75at the tail post.

To document this variation, we drawtwo graphs (preferably on 1/10-inch

graph paper) representing the vari-ations of top and bottom K factor fromnose to tail. Like other contours, theseshould be smooth; kinks in the K-factorvariation will show up as kinks in thebody. Drawing the graphs is simple; thehorizontal axis represents the bodylength, the vertical axis is marked offfrom .5 to 1.0, and we mark three orfour known points and then use a splineor French curve to connect themsmoothly.

When we have these two graphsdrawn, we convert them into coniesexactly as we did the moldlines; in thiscase, the Y axis values are K factorsrather than waterlines or buttlines, andthe segments have their own K factors(not to be confused with the K factorsof the fuselage sections they repre-sent). Figure 4 shows the bottom K fac-tor (BK) graph for DLR, together withthe frames used to break it into conicsegments.

Having collected all these data, weenter them in a file which we'll call, forargument's sake, DLR.LFT. This is aplain ASCII text file which we write withour word processing program. Figure 5shows part of the completed data file,which has six data groups in all (BW,WW, TW, MB, BK, and TK). These areall of the parameters for the body; whenFLOFT reads this file, it can im-mediately report the coordinates, inthree dimensions, of all points on the

56 SEPTEMBER 1990

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surface of the body. It can generatecontour maps, vertical, horizontal andoblique cross-sections, measurementsof surface area and volume, lines of in-tersection between this body and anyother lofted body, and graphs of theradius of curvature of the variousholdlines along the length of the body.

This last feature is a very useful one,because our first cut at a shape maynot be as geometrically smooth as wewould like. Remember, we simply drewthe airplane on a piece of paper andconverted it into a computer model.Each segment is smooth, but how welldo they blend into one another? Werethe curves we drew really optimal, anddid we break them into segments in thebest possible way?

Figure 6 shows the moldline radii forTW, BW, and MB for our first cut. Doyou see how broken and scalloped thelines are? Scallops indicate long sur-face waves not yet apparent to the eye;steps indicate sudden discontinuities inradius of curvature. Whether these im-perfections would have significant aes-thetic or aerodynamic consequenceswe don't know; but John and I both feltintuitively that it is worthwhile to smooththe radius graphs.

FLOFT includes an EDIT commandwhich enables you to break curve seg-ments into two or combine two into one,change K factors, and change the loca-tions, angles, and points of tangency offrames. With a little experimenting you

can smooth out the radii graphs, at thesame time refining your data set. Whenyou superimpose the corrected shapeon the original one, you realize that thecurves that looked fair to you on the firstgo-around actually left considerableroom for improvement. I think of this asthe digital equivalent of the pattern-maker's stroking and eyeballing process.

On the first cut illustrated here, I de-liberately incorporated the canopy in thebody loft for the sake of pointing out apitfall of that approach. Figure 7 showsa contour map (top view) of thewindshield. Note its bluntness, whichcomes from the fact that it has the sameK factor as the fuselage top ahead of it.Many airplanes are lofted this way, butit's better to loft the canopy as a sepa-rate body, streamlined in the front andblending smoothly into the fuselage atthe rear. Figure 8 shows the contour mapof such a canopy, and Figure 9 showshow the radii graphs for the canopymerge into those of the fuselage.

You have now seen how FLOFTworks, and you perhaps understandwhy it is such a convenience. Part of itsvalue is that it puts all the informationyou ever need for tooling and draftingat your fingertips; in fact, it can producecoordinate files that can be read by Au-toCAD and incorporated directly intoengineering drawings.

Another part of its value is that it givesyou a means of making changes to yourdesign by simply changing one or two

numbers in the data file. For example,when it turned out that the spark plugson John's airplane were outside thecowling contours, reshaping the cowl-ing was just a matter of changing twoor three numbers in the first segmentdata for the Top K Factor. DLR has un-dergone some 16 revisions (plus sev-eral smoothing operations) since thefirst sketch as various requirements forclearance and aerodynamic fairnessbecame apparent, and I think Johnwould agree that the work was as nearlyeffortless as it could be.

FLOFT runs on IBM PC's and com-patibles with at least 256 kilobytes ofmemory. It can be used entirely in textmode, directing numerical output to aprinter or to the screen; but it is muchmore powerful and more pleasant touse with a graphics display (which canbe EGA, VGA, or Hercules, with resolu-tions from 640x350 to 800x600 pixels).It can drive plotters that understandHewlett-Packard Graphics Language(HP-GL). FLOFT does not require amath coprocessor, but it must do hugenumbers of calculations and so runsmuch faster with one than without.

FLOFT, together with the supportprograms XING, POLATE, and SEEKK,sample data files and complete (thoughterse) documentation, costs $185 andcan be ordered on 5.15- or 3.5-inchdisks. My address is 1613 Altivo Way,Los Angeles, CA 90026 (phone 2137665-1397).

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