Notes on the design of ailerons

Recent data have shown that certain forms or types of ailerons that are in extensive use are in reality quite inefficient and entirely unsuited for the high speeds now realized. The same data indicate that two forms (both shown here) are efficient and satisfactory in every way. The most important characteristics of ailerons are effectiveness under all flight conditions, small moments about the hinge, high efficiency (small yawing moment opposing turn), and simplicity in construction. Information required for the design of ailerons is given for chord, span, area, and plan form

F-5-L Boat Seaplane : performance characteristics

Performance characteristics for the F-5-L Boat Seaplane are given. Characteristic curves for the RAF-6 airfoil and the F-5-L wings, parasite resistance and velocity data, engine and propeller characteristics, effective and maximum horsepower, and cruising performance are discussed

Comparative performance with direct and geared engines

Comprehensive tests were made to compare the performance of the F-5-L Boat Seaplane fitted with direct drive and Liberty engines. Details are given on the test conditions. The conclusions of the comparison tests follow. 1) An F-5-L with geared engines takes off in approximately 90 percent of the time required for the same airplane with standard direct drive engines. An F-5-L with geared engines climbs in 20 minutes to an altitude approximately 20 percent greater than that obtained with the standard direct drive on the same airplane. 3) There is a large difference between the climbs of the two airplanes of the same type. This difference will always be more pronounced when the climb is normally slow. In the case of the F-5-L airplanes under construction, it is of the order of a 10 percent difference in altitude on a 20 minute climb. 4) The maximum speed of an F-5-L with geared engines is about 3.5 percent greater than the maximum speed of the same airplane with standard direct drive engines (at the same engine r.p.m.). 5) The fuel consumption is probably less effected by the type of drive than by inherent differences in the performance of different airplanes

Boundary critical behaviour at mm-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes

The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent $\Phi$ and related ones are determined to first order in \epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already at first order in $\epsilon$. The \Or(\epsilon) term of $\eta_\|^{\rm sp}$ is found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and the bulk exponent $\beta$ is of order $\epsilon^2$.Comment: 21 pages, one figure included as eps file, uses IOP style file

Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes

The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$ of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda} \sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a dimensionless (renormalized) coupling constant $\lambda$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (\theta-1)$, where $\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos correcte

Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

We investigate the density profile in a driven diffusive system caused by a plane particle source perpendicular to the driving force. Focussing on the case of critical bulk density $\bar{c}$ we use a field theoretic renormalization group approach to calculate the density $c(z)$ as a function of the distance from the particle source at first order in $\epsilon=2-d$ ($d$: spatial dimension). For $d=1$ we find reasonable agreement with the exact solution recently obtained for the asymmetric exclusion model. Logarithmic corrections to the mean field profile are computed for $d=2$ with the result $c(z)-\bar{c} \sim z^{-1} (\ln(z))^{2/3}$ for $z \rightarrow \infty$.Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.

Surface critical behavior of driven diffusive systems with open boundaries

Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the critical particle density in the bulk. The scaling behavior of correlation and response functions is governed by a new exponent eta_1 which is related to the anomalous scaling dimension of the chemical potential of the boundary. The new exponent and a universal amplitude ratio for the density profile are calculated at first order in epsilon = 5-d. Some of our results are checked by computer simulations.Comment: 10 pages ReVTeX, 6 figures include

Surface area coefficients for airship envelopes

In naval architecture, it is customary to determine the wetted surface of a ship by means of some formula which involves the principal dimensions of the design and suitable constants. These formulas of naval architecture may be extended and applied to the calculation of the surface area of airship envelopes by the use of new values of the constants determined for this purpose. Surface area coefficients were calculated from the actual dimensions, surfaces, and volumes of 52 streamline bodies, which form a series covering the entire range of shapes used in the present aeronautical practice