A Performance Analysis of Folding Conformal Propeller Blade Designs

NASAs X-57 Maxwell flight demonstrator has a high-lift system that includes 12 fixed- pitch high-lift propellers located upstream of the wing leading edge for lift augmentation at low speeds. These high-lift propellers are only required at low speeds, and to reduce drag, the propeller blades are folded conformally along the nacelles at other operating conditions. The method of designing the high-lift blades permits several variations of blade cross-section placement along the nacelle surface and a comparative performance analysis was needed to determine if any particular design showed significant benefits. We analyzed the performance of three conformal high-lift propeller designs and compared them to that of a non-conformal baseline propeller to establish both the benefit of stowable blades and the value of each variation. In this study, we first performed a drag analysis of each design in the stowed configuration at the X-57 cruise speed and altitude to determine the drag benefits of each conforming method. Then, among blade designs we compared the thrust, power, and lift for a given input shaft speed to establish any performance losses from the baseline. This analysis shows that the conformal blade designs do not have any appreciable performance losses compared to the baseline blades. Moreover, although the drag in the cruise condition is significantly less than for the non-folding baseline, the drag benefits of each conforming blade approach are similar and the value of each approach largely depends on the ease of integration into the nacelle. This paper presents the results of these studies and discusses the benefits and drawbacks of implementing the conformal blade designs. Specifically, we demonstrate that folding, conformal propeller blades contribute significantly less to cruise drag when compared to windmilling, with an increase relative to a. We also show a less than 1% difference in performance formal, folding propellers and the non-conforming baseline propeller

Concordance of Bing doubles and boundary genus

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature $\sigma$, then the n-iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than $2^{n-1}\sigma$. The same result holds with $\sigma$ replaced by $2\tau$, twice the Ozsvath-Szabo knot concordance invariant.Comment: 13 pages, 7 figure

Surgery description of colored knots

The pair (K,r) consisting of a knot K and a surjective map r from the knot group onto a dihedral group is said to be a p-colored knot. D. Moskovich conjectured that for any odd prime p there are exactly p equivalence classes of p-colored knots up to surgery along unknots in the kernel of the coloring. We show that there are at most 2p equivalence classes. This is a vast improvement upon the previous results by Moskovich for p=3, and 5, with no upper bound given in general. T. Cochran, A. Gerges, and K. Orr, in "Dehn surgery equivalence relations of 3-manifolds", define invariants of the surgery equivalence class of a closed 3-manifold M in the context of bordisms. By taking M to be 0-framed surgery of the 3-sphere along K we may define Moskovich's colored untying invariant in the same way as the Cochran-Gerges-Orr invariants. This bordism definition of the colored untying invariant will be then used to establish the upper bound.Comment: 41 pages, 23 figures (Version 3) Minor revisions and typos fixed. Proofs of Propositions 4.1 and 4.8 revise

Seifert forms and concordance

If a knot K has Seifert matrix V_K and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non-concordant knots having Seifert matrix V_K.Comment: Shortened version containing the main examples, published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper14.abs.htm