Wing Sections and Laminar Flow

At a glance

Category: A summary-and-correlation report: part handbook, part review. It adds some original method (the derivation of the 6-series thickness forms, and a rapid hand method for pressure distributions) and a large supplement of design data. In the authors' words, its aim is to summarize these data and to correlate and interpret them insofar as possible (p. 1).
Context: It builds on NACA Report 460 (Jacobs, Ward & Pinkerton, 1933) for the four-digit family, Theodorsen's conformal-mapping theory of arbitrary airfoils, classical thin-airfoil theory, Allen's simplified pressure method, and von Kármán's 1941 compressibility work. Most of its data come from Langley's new two-dimensional low-turbulence tunnels.
Contributions: One catalogue and naming system for the NACA four-digit, five-digit, 16-, 6- and 7-series airfoils.
Published methods for deriving the 6- and 7-series thickness forms by conformal mapping, including the closed-form a mean lines of eq. (6).
A rapid superposition method, eq. (14), for estimating pressure distributions by hand, with the data it needs tabulated for every section.
Systematic smooth and rough two-dimensional data at Reynolds numbers up to 9 million, and higher for some sections.
The central finding: surface condition affects lift and drag at least as much as airfoil shape. It comes with practical finish criteria: No. 320 sandpaper, a straightedge test, and hand inspection for specks.

The report, section by section

Summaryp. 1

Recent airfoil data, mostly from the Langley two-dimensional low-turbulence pressure tunnel plus wake-survey flight measurements, are collected and correlated. Detailed design data are given for the NACA 6-series, with recent data for the 00-, 14-, 24-, 44- and 230-series. The report covers how the 6- and 7-series shapes were derived, how to estimate pressure distributions quickly, and lift, drag, moment, critical speed, surface condition and high-lift devices.

Most of the data on airfoil section characteristics were obtained in the Langley two-dimensional low-turbulence pressure tunnel.Summary, p. 1

The headline is a warning as much as a result. Laminar-flow sections give much lower drag if, and only if, the wing surfaces are sufficiently smooth and fair.

Introduction and Symbolspp. 1–2

Earlier results were scattered across reports with limited objectives, which had prevented adequate analysis and interpretation. Numbered figures illustrate the text, while the design data sit in five unnumbered supplements (I–V) arranged by airfoil (p. 1). Two pressure coefficients recur throughout. $P = (p - p_{0}) / q_{0}$ is the usual one. $S = (H_{0} - p) / q_{0} = 1 - P$ equals $(v / V)^{2}$ at low speed, so $S > 1$ means local suction. $P_{R}$ is the resultant load (lower minus upper surface).

Historical Developmentpp. 2–3

Systematic work on the four-digit family began in 1929 in Langley's Variable-Density Tunnel, with every section sharing one thickness distribution. A forward-cambered five-digit family followed. Some of its sections showed a large sudden loss in lift at the stall. Comparing drag at low lift with flat-plate skin friction showed that nearly all profile drag was skin friction. Lower drag therefore meant keeping the boundary layer laminar further back, which takes favourable pressure gradients and very low stream turbulence.

That led to two new tunnels in which a model spans the narrow test section, removing tip and support corrections. It also led to new shapes. The 16-series was the first low-drag, high-critical-speed family. The 2- to 5-series, designed with approximate theory, were already considered obsolete by 1945: their maximum lift was low, and they assumed more laminar flow than a real surface could keep. The 6-series came from improved conformal-mapping methods, and the 7-series pushes laminar flow onto the lower surface as well (pp. 2–3).

Description of Airfoilspp. 3–7

Method of combining mean lines and thickness distributionsp. 4

Every NACA section is a symmetric thickness form $y_{t} (x)$ wrapped around a mean (camber) line $y_{c} (x)$ . The thickness is laid off perpendicular to the mean line, whose local slope is $tan θ = d y_{c} / d x$ :

x_{U} = x - y_{t} sin θ, y_{U} = y_{c} + y_{t} cos θ, x_{L} = x + y_{t} sin θ, y_{L} = y_{c} - y_{t} cos θ

(1)–(4)

The leading-edge radius is centred on a line through the chord's end with the mean-line slope there. For mean lines with an infinite leading-edge slope, the slope at $x / c = 0.005$ is used. So cambered sections poke slightly ahead of the leading-edge point.

Diagram of a cambered airfoil showing mean line, chord line, leading-edge radius and a sample calculation table — Figure 1. The construction, with a sample calculation for the NACA 65,3-818, a = 1.0.

NACA four-digit series airfoilspp. 4–5

In a designation such as NACA 2415, the first digit is the maximum camber in percent of chord, the second its position in tenths of chord, and the last two the thickness in percent. Report 824 tabulates the shapes but does not print their equations. Those come from Report 460 (1933). The thickness of a section with thickness ratio $t$ is

\pm y_{t} = \frac{t}{0.20} (0.29690 x - 0.12600 x - 0.35160 x^{2} + 0.28430 x^{3} - 0.10150 x^{4})

$x$ in fractions of chord. Maximum thickness falls at 30% chord, and the trailing edge keeps a small finite thickness (0.126% of chord for the 0012).

The mean line is two parabolas, with maximum camber $m$ at position $p$ : $y_{c} = \frac{m}{p ^{2}} (2 p x - x^{2})$ ahead of $p$ and $y_{c} = \frac{m}{( 1 - p ) ^{2}} [(1 - 2 p) + 2 p x - x^{2}]$ behind it. Thicker or thinner forms scale linearly, and the leading-edge radius varies as the square of the thickness ratio: 1.58% of chord for the 0012 (p. 5).

section outline
mean line
Report 824 ordinates, printed p. 100

Max camber · 1st digit 2% c

Camber position · 2nd digit 40% c

Thickness · last two 12% c

Designation: NACA 2412
L.E. radius: 1.58% c
Max t at: 30% c

x %c	upper	rpt	lower	rpt
1.25	2.16	2.15	-1.65	-1.65
2.50	2.99	2.99	-2.27	-2.27
5.00	4.13	4.13	-3.00	-3.01
7.50	4.97	4.96	-3.46	-3.46
10.00	5.63	5.63	-3.76	-3.75
15.00	6.61	6.61	-4.10	-4.10
20.00	7.26	7.26	-4.23	-4.23
25.00	7.67	7.67	-4.22	-4.22

x %c	upper	rpt	lower	rpt
30.00	7.88	7.88	-4.13	-4.12
40.00	7.80	7.80	-3.80	-3.80
50.00	7.24	7.24	-3.35	-3.34
60.00	6.35	6.36	-2.78	-2.76
70.00	5.18	5.18	-2.15	-2.14
80.00	3.75	3.75	-1.50	-1.50
90.00	2.07	2.08	-0.83	-0.82
95.00	1.13	1.14	-0.48	-0.48

Figure 14. Any four-digit section, rebuilt from the Report 460 equations and the construction of eqs. (1)–(4). For the 0012 and 2412, the gold points and columns show the ordinates Report 824 printed.

NACA five-digit and 1-series airfoilsp. 5

In the five-digit 23012, the first digit × 3/2 gives the design lift coefficient in tenths ( $c_{l_{i}} = 0.3$ ). The next two digits, halved, give the maximum-camber position in percent of chord (15%), and the last two the thickness (12%). The family uses the four-digit thickness forms with forward-cambered mean lines. The 1-series, such as the 16-212, gives the minimum-pressure position in tenths of chord (6), then the design lift in tenths (0.2), then the thickness. It is normally cambered with the $a = 1.0$ mean line. (These are two headings in the report, merged here.)

NACA 6-series airfoilspp. 5–7

Take the NACA 65,3-218, a = 0.5. The 6 is the series. The 5 is the minimum-pressure position in tenths of chord on the symmetric form at zero lift. The 3 is the half-width, in tenths, of the lift range over which favourable gradients exist on both surfaces. The 2 is the design lift coefficient in tenths, and 18 the thickness. Leaving out $a$ implies $a = 1.0$ .

The a mean lines carry a load that is uniform from the leading edge to $x / c = a$ and then falls linearly to zero at the trailing edge. Their shape has a closed form:

\frac{y _{c}}{c} = \frac{c _{l_{i}}}{2 π ( a + 1 )} {\frac{1}{1 - a} [\frac{1}{2} (a - x)^{2} ln ∣ a - x ∣ - \frac{1}{2} (1 - x)^{2} ln (1 - x) + \frac{1}{4} (1 - x)^{2} - \frac{1}{4} (a - x)^{2}] - x ln x + g - h x}

(6)

$g = - \frac{1}{1 - a} [a^{2} (\frac{1}{2} ln a - \frac{1}{4}) + \frac{1}{4}]$ , $h = \frac{1}{1 - a} [\frac{1}{2} (1 - a)^{2} ln (1 - a) - \frac{1}{4} (1 - a)^{2}] + g$ . The ideal angle of attack is $α_{i} = - h c_{l_{i}} / [2 π (a + 1)]$ .

Load parameter a 0.5Load is uniform back to x/c = a, then falls linearly to zero.

Design lift c_li 0.40Ordinates and α_i scale linearly with c_li.

IDEAL ANGLE α_i: 1.22deg
c_m,c/4: -0.056
Max camber: 3.00% c
At x/c: 0.45

Figure 15. Eq. (6) evaluated live. The trapezoidal load (top) produces the mean line (bottom). At

a = 0.5

and

c_{l_{i}} = 1

the readouts show the report's tabulated design values for that line,

α_{i} = 3.04°

and

c_{m, c /4} = - 0.139

The 7-series (for example 747A315) gives the extent of favourable gradient on the upper and lower surfaces separately (4 and 7 tenths), plus a serial letter. Its mean lines are sums of a lines. The 747A315 uses $a = 0.4$ at 0.763 and $a = 0.7$ at −0.463, which add up to its design lift of 0.3 (Table I, p. 7).

Theoretical Considerationspp. 8–15

Pressure distributionspp. 8–13

The 6-series thickness forms were designed rather than found by trial. Theodorsen's method maps a circle to a near-circle and then to an airfoil: $z = a e^{ψ_{0} + i ϕ}$ , $z^{'} = a e^{ψ + i θ}$ , $ζ = z^{'} + a^{2} / z^{'}$ . The designer chooses $d ε / d ϕ$ , integrates to find the shape, and iterates. The velocity at the surface is

\frac{v}{V} = \frac{[ sin ( α _{0} + ϕ ) + sin ( α _{0} + ε _{T} ) ] e ^{ψ_{0}}}{( sinh ^{2} ψ + sin ^{2} θ ) [ ( 1 - \frac{d ε}{d ϕ} ) ^{2} + ( \frac{d ψ}{d ϕ} ) ^{2} ]}

(13)

One design lesson stands out: there is an optimum leading-edge radius. Too small, and a suction peak forms right at the nose. Too large, and the peak sits a few percent behind it. Simply scaling a form's ordinates to make it thicker lowers its critical speed unnecessarily, which is why later families scale the mapping functions instead (pp. 8–9).

Theoretical pressure distributions for basic 6-series sections varying thickness and minimum-pressure position — Figure 2. Basic 6-series forms at zero lift: (a) more thickness raises the peak; (b) moving minimum pressure aft lengthens the favourable gradient.

Three-dimensional plot of pressure distribution against chord position and lift coefficient for the NACA 65-015 — Figure 3. The 65₂-015 at increasing lift. The flat forward slope of the upper surface disappears at $c_{l} \approx 0.22$ , the end of the low-drag range, and a leading-edge peak grows.

Rapid estimation. For design work the report superposes three tabulated velocity increments: the basic thickness form at zero lift ( $v / V$ ), the mean line's design load ( $Δ v / V$ ), and an additional load from angle of attack ( $Δ v_{a} / V$ ):

S = (\frac{v}{V} \pm \frac{Δ v}{V} \pm \frac{Δ v _{a}}{V} f (α))^{2}, f (α) \approx c_{l} - c_{l_{i}}

(14), (15)

Upper signs for the upper surface. Increments at the same $x$ are added and assigned to the surface point at that $x$ .

upper surface
lower surface
report example 3: 1.712 / 1.032

Section NACA 24120012 thickness with the 64 mean line scaled by 2/6 (design c_l = 0.253).

Section lift c_l 0.50Additional-load factor f(α) = c_l − c_li = 0.247

S upper @ 0.30c: 1.710
S lower @ 0.30c: 1.033
Peak S: 1.93
Critical Mach: 0.60

Set c_l to 0.50 to see the report's worked example. The critical Mach number uses the Kármán–Tsien rule behind the report's supplement IV chart. It is only computed at the tabulated stations, so a sharp leading-edge peak may be missed.

Figure 4. Eq. (14) with the report's own tables: the NACA 0012 thickness form and the 64 mean line scaled by

m /6

. Set the 2412 to

c_{l} = 0.5

to see the report's worked example 3 (S = 1.712 upper, 1.032 lower at 30% chord). The peak suction sets the critical Mach number.

Upper and lower surface pressure distributions, theory line against experimental points, for the NACA 66(215)-216, a = 0.6 — Figure 5. The first approximation against measured pressures on the 66(215)-216, a = 0.6 at $c_{l} = 0.23$ . Agreement is close while the boundary layer is thin.

Critical Mach numberpp. 13–14

The critical Mach number is the free-stream Mach number at which the surface flow first reaches sonic speed. It is predicted from the peak low-speed $S$ with von Kármán's compressibility rule, and supplement IV charts the result. It predicts where sonic flow first appears, but not where large changes in characteristics occur, especially with sharp nose peaks. The 6-series reaches considerably higher maximum critical Mach numbers than the 24-, 44- and 230-series of equal thickness. On that chart, the 0012 at zero lift (peak $S = 1.41$ ) first reaches sonic flow at about Mach 0.73.

Moment coefficients and angle of zero liftp. 14

Both come from thin-airfoil theory via the mean-line tables and scale with camber: the NACA 4415 has $c_{m, c /4} = - 0.157 \times 4/6 = - 0.105$ . With the thin-airfoil lift slope of $2 π$ per radian, the angle of zero lift in degrees is

α_{l_{0}} = α_{i} - \frac{57.3}{2 π} c_{l_{i}}

(16)

For the 2415: $α_{i} = 0.74 \times 2/6 = 0.25°$ and $c_{l_{i}} = 0.253$ , so $α_{l_{0}} = - 2.0°$ . The report warns against using such values to set washout without experimental verification.

Description of flow around airfoilsp. 15

At low and moderate lift on a smooth section, the boundary layer stays laminar to about the first minimum-pressure point, then separates and reattaches almost immediately as turbulent flow. Drag is mostly skin friction, set by how much of the surface stays laminar. Raising the angle of attack moves the upper-surface minimum pressure forward. On 6-series sections transition jumps forward suddenly at the end of the low-drag range, which produces the characteristic drag bucket. At high lift, separation and form drag take over.

Experimental Characteristicspp. 16–51

The primary source is the Langley two-dimensional low-turbulence pressure tunnel, with design data from 2-foot-chord models. Flight drag comes from wake surveys on wings or gloves, reduced with compressible-flow methods (p. 16).

Drag characteristics of smooth airfoilspp. 16–22

In the low-drag range, drag depends mainly on Reynolds number and the extent of laminar flow, and only moderately on thickness and camber. Moving minimum pressure aft cuts minimum drag steadily: at $R = 6 \times 1 0^{6}$ , from roughly 0.005 for the 63-series toward 0.0035 for the 67-series (Fig. 9). The theoretical low-drag range is about 0.2 in $c_{l}$ for 12% thickness, widening by about 0.2 for every 3% of extra thickness. At $R = 35 \times 1 0^{6}$ it shrinks to about one-half the theoretical value (Fig. 14).

Log plot of minimum section drag coefficient against Reynolds number for several airfoils, with laminar and turbulent flat-plate lines — Figure 6. Minimum drag against Reynolds number, with flat-plate laminar and turbulent friction lines. The 65₃-418 is worse than the 0012 at low R, because of laminar separation, and better at high R. Low-Reynolds-number data can mislead.

Drag coefficient against lift coefficient for four 64-series sections showing low-drag buckets — Figure 7. Drag *buckets* of 64-series sections cambered to $c_{l_{i}} = 0.4$ , at $R = 9 \times 1 0^{6}$ .

The report also tests effective aspect ratio as a selection figure, fitting $C_{D} = C_{D, L = 0} + k C_{L}^{2}$ through polars at $C_{L} = 0.2$ and 1.0 (eq. 17). For an aspect-ratio-10 airplane the 23018 scores 9.29 but a maximum $L / D$ of 18.5, while the 65₃-418 scores worse (8.30) yet reaches $L / D = 19.8$ . Effective aspect ratio, the report concludes, is not a satisfactory criterion for choosing a section (p. 21).

Effect of surface irregularities on dragpp. 22–30

This is the most practical part of the report. Large models were finished by sanding chordwise with No. 320 carborundum paper. Polishing or waxing a properly sanded surface gave no further gain. Protuberances are worse than dents, and dust on a fingerprint can trip transition. Turbulence spreads behind a disturbance in a wedge of about 15°. Fairness is checked with a straightedge rocked chordwise: it should move without jarring or clicking.

Drag coefficient against Reynolds number for a 60-inch-chord model in smooth and painted conditions — Figure 8. A 60-in.-chord 65(421)-420 model, smooth versus with unimproved camouflage lacquer. The painted surface loses its low drag suddenly near $R = 20 \times 1 0^{6}$ .

To compare sections fairly when rough, the report defines a standard roughness: 0.011-inch carborundum grains applied to the airfoil surface at the leading edge over a surface length of 0.08c … thinly spread to cover 5 to 10 percent of this area. That is worse than ordinary manufacturing flaws but milder than ice, mud or combat damage (p. 24).

Wing sections built like real aircraft, delivered to the tunnel without special finishing, showed minimum drag of the order of 0.0070 to 0.0080 in nearly all cases regardless of section. None was fair at the front spar. One 66-series specimen with no spar ahead of about 35% chord kept low drag up to $R \approx 30 \times 1 0^{6}$ (pp. 24–29).

Photograph of a large wing section model cut open to show internal ribs and spars — Figure 16. A 100-in.-chord practical-construction model, opened to show its internal structure (LMAL 36795).

Photograph of a wooden NACA 23016 wing model with a simulated door joint across its upper surface — Figure 17. A NACA 23016 model with a simulated door joint (LMAL 37918), tested as received, with grey primer, and with camouflage paint.

Lift characteristics of smooth airfoilspp. 30–37

Angle of zero lift is set mostly by camber, with thickness having little effect. Measured values relative to thin-airfoil theory are about 0.93 for the four-digit series, 1.08 for the 230-series and 0.74 for 6-series sections with the uniform-load mean line (p. 30). Lift-curve slope for 6–10% sections of the four-digit, five-digit and 64-series is very close to the thin-airfoil value of $2 π$ per radian, 0.110 per degree. It falls with thickness for the older families and rises for the 6-series.

thin-airfoil theory, 2π per radian
α_L0, theory
measured α_L0 ≈ 0.93 × theory = -1.93° (Rpt. 824 correlation)
c_l at the chosen α

Angle of attack 4.0°

α_L0, THEORY: -2.08deg
α_L0 × 0.93: -1.93deg
c_l AT α: 0.666
c_m,c/4: -0.053

Figure 9. Thin-airfoil lift for four-digit sections, with the report's measured correction for zero-lift angle (× 0.93) marked in gold. Real sections stall, which theory cannot show.

Five panels of lift-curve slope against thickness ratio for several NACA families, smooth and rough — Figure 10. Measured lift-curve slope against thickness, smooth and with standard roughness, at $R = 6 \times 1 0^{6}$ .

Maximum lift. At $R = 6 \times 1 0^{6}$ the plain four- and five-digit sections peak at 12% thickness. The best combination overall is about 12% thick with $c_{l_{i}} = 0.4$ . Raising $R$ from 3 to 9 million adds roughly 0.15–0.20 to $c_{l, ma x}$ for the 24-, 44- and 230-series. A rectangular wing of aspect ratio 6 is predicted to reach 4–7 percent less than its section $c_{l, ma x}$ (pp. 33–37).

Lift characteristics of rough airfoilspp. 37–39

Leading-edge roughness cuts $c_{l, ma x}$ heavily, by about the same amount with or without a 60° split flap, and lowers the lift-curve slope, especially for thick sections with minimum pressure far aft. A full-scale fighter in service condition reached a $C_{L, ma x}$ more than 0.2 lower than its tunnel model. Sealing leaks helped. Roughness strips behind 20% chord barely mattered.

Unconservative airfoilspp. 39–40

An unconservative section is excellent when smooth but has excessive drag at climb and cruise lift when rough. The report's yardstick is the lift coefficient at which the rough-leading-edge drag reaches 0.02. It peaks at 12–15% thickness and drops as minimum pressure moves aft. That matters for thick root sections on long-range airplanes.

Pitching moment and aerodynamic centerpp. 40–43

Measured $c_{m, c /4}$ for 6-series sections with $a = 1.0$ is about three-quarters of the theoretical value. The older families also fall short of theory but agree better. The aerodynamic center lies slightly ahead of the quarter chord for the 24-, 44- and 230-series and slightly behind it for the 6-series (about 0.25–0.28c), moving further as thickness grows (pp. 40–43).

Scatter plot of measured against theoretical moment coefficient for several NACA airfoils with a line of perfect agreement — Figure 11. Measured against theoretical quarter-chord moment coefficients. Points below the line mean less nose-down moment than theory, most strongly for the uniform-load 6-series sections.

High-lift devicespp. 43–47

On 6-series sections, a 0.25c single slotted flap on the 63,4-420 reached $c_{l, ma x} \approx 2.95$ , and a 0.309c double slotted flap on the 65₃-118 reached 3.28. The report concludes no special difficulties exist in obtaining high maximum lift with slotted flaps on moderately thick 6-series sections. Split-flap increments on 12% sections were only about three-quarters of those on a 16% section.

Drawing of an airfoil with a double slotted flap retracted and deflected 65 degrees, with pivot dimensions — Figure 12. The double slotted flap on the 65₃-118, retracted and deflected 65°, with its pivot geometry.

Table 1. Excerpt from Table II: three-dimensional wings in the 19-ft pressure tunnel (pp. 64–67).

Model	Sections	Flaps	R × 10⁻⁶	C_L,max	Stall
I	66(215)-216, A = 7	none	4.6	1.41	abrupt, root to tip
I	66(215)-216	split 60°, 0.20c, inboard + outboard	4.6	2.51	abrupt, root to tip
II	66(215)-116 / -216, λ = 0.5	Fowler 30° / 30°	3.4	3.29	extremely abrupt
VII	Mod. 65,3-318 / 65(318)-316	double slotted 55° / 30°	5.1	2.85	satisfactory
XV	23015.6 / 23009	slotted 50°	5.6	2.52	very abrupt

Stall notes in Table II range from satisfactory to extremely abrupt, depending on planform and flap arrangement.

Lateral-control devices, leading-edge air intakes, and interferencepp. 43–51

Three short sections, merged here. Aileron effectiveness falls below thin-airfoil theory, with no large consistent dependence on section shape. Leading-edge air intakes can work but cannot yet be designed without experimental development. Interference with fuselages and nacelles is similar for conservative 6-series sections and other good airfoils.

Application to Wing Designpp. 51–52

Section data feed lifting-line methods for zero-lift angle, lift slope, moment and drag. Choose the root section as thick as is aerodynamically feasible. For high-speed airplanes the critical Mach number is the binding limit; for slower ones it is drag with a rough surface. The tip section wants high $c_{l, ma x}$ and a gentle stall, so camber is the main lever there. Forward camber (the 230-series) risks sudden stall. Suggested pairings are a 230-series root with a 44-series tip, or a 63-series root with a 65-series tip. High taper combined with large sweep is singled out as particularly bad.

Conclusionspp. 52–53

Laminar-flow 6- and 7-series sections cut drag at high-speed and cruise lift only with fair, smooth surfaces.
Full-size wings can get extensive laminar flow when sanded chordwise with No. 320 carborundum paper and free of specks.
With current construction, moderately thick wings reach $c_{d, min}$ of the order of 0.0080, set by surface condition rather than section.
Smoothing pays at high Reynolds number even without laminar flow.
Smooth, moderately cambered 6-series sections ( $a = 1.0$ ) reach $c_{l, ma x}$ as high as the 24- and 44-series.
With flaps, thick 6-series sections match the 23012's $c_{l, ma x}$ , but thinner ones fall well short.
6-series lift-curve slopes slightly exceed those of the older families and usually exceed thin-airfoil theory.
Leading-edge roughness causes large $c_{l, ma x}$ losses, the same with or without split flaps.
Roughness lowers the lift-curve slope, most for thick sections with minimum pressure aft.
Predicting a real wing requires knowing its surface condition.
6-series sections have higher critical Mach numbers at cruise lift. (Points 12–15 cover high-lift critical speed, ailerons, interference and intakes.)

Appendix: Methods of Obtaining Data in the Langley Two-Dimensional Low-Turbulence Tunnelspp. 54–60

Two closed-throat tunnels, the LTT and the TDT, share a 3 ft × 7½ ft test section. A contraction of about 20:1 and fine screens keep turbulence to only a few hundredths of 1 percent. The TDT runs at up to 10 atmospheres and about 300 mph at atmospheric pressure. Standard tests use 2-ft-chord wooden models at up to $R \approx 9 \times 1 0^{6}$ (at 4 atmospheres). Lift comes from floor and ceiling pressures, drag from a wake-survey rake, and moments usually from a balance (p. 54).

Lift. The model's lift appears as a pressure reaction on the floor and ceiling, integrated over about 13 ft by an integrating manometer. Because the orifices cannot extend to infinity, the reading is a fraction $η$ of the true lift. That fraction is found from an image system of vortices that mimics the tunnel walls:

u = \frac{Γ}{2 h _{T}} sech \frac{π x}{h _{T}}, P_{R} = \frac{4 u}{V}, c_{l}^{'} = \frac{c _{l_{T}}}{η _{a}} - (\frac{η _{b}}{η _{a}} - 1) c_{l_{i}}

(19), (20), (24)

$h_{T}$ is the tunnel height. For a 2-ft model, $η_{a} = 0.9296$ for the additional load and $η_{b} \approx 0.932$ –0.935 for the basic load, depending on $a$ .

Sketch of a point vortex between upper and lower tunnel walls with an infinite row of image vortices — Figure 13. The image system used to correct the floor-and-ceiling lift measurement.

Drag. A rake of total-pressure tubes surveys the wake behind the model. The drag coefficient follows from the momentum deficit, corrected with a factor $K$ that assumes a Gaussian wake profile (eqs. 25–27).

Wall corrections. The walls speed up the flow past the model (blocking) and curve the streamlines. For a model of chord $c$ in a tunnel of height $h_{T}$ , $σ = \frac{π ^{2}}{48} (c / h_{T})^{2}$ , which is 0.0146 for a 2-ft model. With $Λ$ a shape factor and $ξ \approx 0.002$ for the static-orifice position, the corrections are

c_{l} = [1 - 2Λ (σ + ξ) - σ] c_{l}^{'}, c_{d} = [1 - 2Λ (σ + ξ)] c_{d}^{'}

(37), (40)

Looking ahead

Assumptions and open questions

Key assumptions

Eq. (14) adds the thickness, camber and angle-of-attack effects on surface velocity linearly. The authors note this superposition has inadequate theoretical justification yet works well in practice (p. 11).
The additional load is scaled by $f (α) = c_{l} - c_{l_{i}}$ , treating the tabulated $Δ v_{a} / V$ as corresponding to a unit additional lift coefficient, which it does only approximately (p. 5).
Mean-line design values ( $c_{l_{i}}$ , $α_{i}$ , $c_{m, c /4}$ ) come from thin-airfoil theory, which ignores thickness and the boundary layer.
Wake-survey drag assumes a Gaussian total-pressure profile and uniform static pressure across the wake (eqs. 25–27).
A single standard roughness stands in for service deterioration, and permissible roughness is presumed to scale with chord (pp. 22–24).
Most measurements are at Reynolds numbers of 3 to 9 million (p. 52).

Where further work would help

Flight Reynolds numbers. The low-drag range keeps shrinking with Reynolds number (to about half its theoretical width at 35 million), so applying the 3–9 million data to larger, faster airplanes calls for tests at higher Reynolds number.
Real surfaces. The report shows surface condition matters at least as much as shape. How a given production finish, paint system or level of wear maps onto the standard roughness would need direct measurement.
Three-dimensional wings. Section data feed lifting-line methods, but Table II's stall behaviour varies with planform and flap arrangement. The report itself asks for systematic high-Reynolds-number three-dimensional data (p. 37).
Gaps in the families. Mean lines with $a < 0.5$ , quantitative waviness criteria, and design rules for leading-edge air intakes are all named as needing further study (pp. 28, 34, 50).
Above the critical Mach number. The critical-Mach predictions mark where sonic flow first appears. What happens beyond it was outside the report's scope.

What happened next

1929
Systematic four-digit tests begin in Langley's Variable-Density Tunnel (Report 824, p. 2).
1933
NACA Report 460 publishes 78 related sections and the four-digit equations.
1942
Jacobs, Abbott & Davidson issue preliminary low-drag data from the low-turbulence tunnels. Report 824's wartime version supersedes it.
1945
Report 824 is signed on 5 March 1945.
1959
Abbott & von Doenhoff's Theory of Wing Sections, including a Summary of Airfoil Data appears from Dover. NASA Langley later called the 1945 report one of the most important NACA reports ever written.

Sources

NACA Report 824 on NTRS · Public use permitted
NACA Report 460: The characteristics of 78 related airfoil sections (1933) · Source of the four-digit equations
NASA Langley: Ira H. Abbott

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