One of the first patents for compensating valve brass instruments by US Letters Patent #457,337 dated 11 August 1891 of Fontaine Besson is studied and optimized to obtain a much better in tune compensating instrument. The variance of intonation for the Besson instrument is 18.86%. An optimized four valve brass instruments is devised that lowers the variance to 4.22%. However, the first valve is flat by 7.39% on both sides of the instrument. Because intonation errors of ±5% are tolerable a spring loaded trigger must be provided to shorten the first valve when used alone. An EXCEL spreadsheet is presented analyzing many different three, four and five valve compensating and noncompensating instruments. Of particular interest is a five valve compensating instrument having a variance of 2.37% and standard deviation of 2.48%. The fifth valve lowers the instrument by 6 semitones. Instead of the fifth valve aforementioned a fifth valve of 0.237 of the length of the fourth valve could be used in combination with the fourth valve making the horn lighter. An Excel spread sheet is presented for the calculations relating to many ordinary and compensating three, four and five valve instruments.

Described here is a design for an F/BBb tuba. The valves and keys needed for a full double tuba take a lot of space. There exists a full and complete double tuba in BBb/EEE built on a very large instrument frame and is more than 5 feet tall and 2 feet wide [1]. However, the sizes of F tuba frames are too small to accommodate 5 double and 2 switch valves and their associated tubing. Using a standard F tuba frame, the lack of space has been solved by having four double valves and two switch valves. The fourth double valve is unusual because it is descending on the F side and ascending on the BBb side of the instrument. An ascent to a BB □tuba is made by the ascending part of that valve. The valve slide lengths have been optimized to yield intonation such that −5< intonation error < 5 cents over a five semitone descent from an open note. Various acoustic measurements are reported for the instrument which will be exhibited. [1] F. J. Young, “Five valve compensating brass wind instrument,” Proc. Meetings Acoust. 11, 035004 (2011).

The optimal valve slide lengths for three valve double and triple brass instruments are investigated to ensure that the errors in intonation never exceed five cents sharp or flat over the range of playing. Using the method of least squares to minimize the intonation errors caused by various common valve combinations, it is shown that tuning the open tone 3.2 cents sharp and making suitable valve slide adjustments yield an overall root mean square error of about 2.6 cents. This calculation does not count the errors resulting with the 13 and 123 valve combinations encountered in the low register of the F side of the horn. At the risk of stuffiness, these notes are often corrected by alteration of the right hand position. The best overall intonation is shown to exist for the triple horn in F, Bb, and high Eb, exhibiting the overall root mean square error of about 2.6 cents. In this case the pedal notes on the high Eb side of the horn are used. They are fingered 12 and 23 for said low G and F#. The more common triple horn in F, Bb, and high F requires the use of the 13 and 123 combinations.

The natural frequencies of circular drum heads are calculated by the use of finite elements. The results for unmuted drum heads are almost identical to the well known analytical solution expressed in Bessel functions. Mutes of various sizes and shapes are used to stop a section of the head from vibrating. For example, a circular damper having one-quarter of the drum head diameter raises the resonant frequencies of the first eight modes of vibration by 11%, 1.7%, 15.1%, 3.8%, 6.2%, 9.2%, 5.2%, and 10.1%. For the undamped drum head, modes two and three are identical. Modes four and five are identical as well as modes seven and eight. Each of the pairs have differing resonant frequencies. The changes in resonant frequencies are strongly influenced by where the mute is placed. It would seem that the calculated frequency changes could be used to musical advantage.

A companion paper shows how a triple brass instrument can be designed to yield a nearly perfect, well tempered intonation. This cannot be easily applied to the larger low-brass instruments because the inertia of triple valves increases as the square of the radius and varies with height. Double piston valves have been used for more than 130 years to change the pitch of large brass instruments. In May 2009, this author presented most of the known 3 and 4 valve systems including compensating ones. However well optimized, they are not in tune within plus or minus 5 cents. To solve this problem an instrument with four double valves and a tritone switch valve is presented and optimized to minimize the rms intonation error. The ratios of slide lengths to the instrument’s length are given by 0.126, 0.0631, 0.198, 0.337, and 0.413. The compensator slide ratios are 0.0522, 0.0261, 0.172, and 0.139. The instrument is to be tuned 3 cents sharp. Descending from the second open tone in semitones, the resulting errors in cents are 3.15, −2.97, −2.81, 2.65, 0, 0, 3.25, −2.97, −2.81, 2.65, 0, and 0. The rms intonation error is 2.37 cents, which is very acceptable in musical performance.

The intonation deviations from the well-tempered scale are presented for valve brass wind instruments. Compensating and full double instruments are considered. Systems including descending valves and less popular ascending valves are studied. The lengths of the valve tubes are optimized by minimizing the overall root mean squared (rms) intonation error using the method established in 1967 [R. Young, J. Acoust. Soc. Am. 42, 224–235 (1967)]. Open note detuning is considered in each case and improves the overall intonation. The worst three valve instrument without open note detuning has an rms deviation 24 cents The best of the three and four valve instruments is a three valve compensating euphonium tuned 3 cents sharp on the open notes and flat on valves 2, 1, and 3 by 3, 3, 10 cents, respectively. It exhibits only 2 cents rms deviation on single valves and less than 3 cents on combinations of valves. The comparisons also include several new three, four, and five valve systems. Included is a double horn with only two double valves and a switch valve.

A euphonium is presented that has better intonation and is easier to play in the extreme registers. It is a complete double horn having five double valves in contrast to the incomplete normal double French horn having only three double valves. The valves descend 2, 1, 3, 4, and 5 semitones from the open tones. The large bell is for the B♭ standard part of the instrument. A switch valve activates the smaller alto bell in the key of high E ♮ and sends the air through the five shorter valve slides and out the small bell. The fundamental frequency of the E side is 82.4 Hz or six semitones above the fundamental of the B♭ euphonium. The key of E rather than F or E♭ enables all notes in the complete range (about 29–988 Hz) to be played with a single tunable valve slide. Either of the other keys would introduce a need for one additional valve or compromise the intonation.

The alphorns built and sold by the late Joseph Littleton of Hammondsport, NY are used in this study. His dimensions of bore as a function of position are used in solution of the Webster equation for impedance solved numerically earlier [F. J. Young, Acustica, 10, 91–97 (1960)]. The musical notation for the frequencies of the impedance peaks are given below. Here the subscripts refer to the harmonic number. The fundamental, rarely used, is 13 cents flat from A at 55 Hz. The intonations errors for. C1, C2, G3, C4, E5, G6, B7b, C8, D9, E10, F11, G12, A13, B14b, B15, C16, C17#, and D18 are 287, 58, 195, 28, 1.5, 0.83, -28, -0.85, -2.63, 1.5, 40, 14, -49, 1, -3, 16, 24 and 28 cents.

The high-frequency performance of capacitors is related to their geometry and material properties. By considering multilayer capacitors as distributed electrical systems, the tools of ICONSIM are applied to study resonant frequencies, equivalent circuits of capacitors, and the influence of ground planes, test fixtures, and type of connection topology. The methods established are applied to well-documented capacitors described in the literature and good agreement between experimental results and analyses is obtained

The electrical design, analysis and performance of tabular capacitors are presented. Simple formulas for capacitances are derived for spiral and concentric type tabular capacitors. By numerical methods the regions of greatest electric stress in the dielectric are found. The influence of bumps on the capacitor plates is examined by the method of conformal transformation. It is shown that a small circular ridge running the length of the capacitor can reduce the voltage rating by 50%. The inductance of the capacitor sets an upper bound on the highest frequency at which the capacitor behaves ideally. It was previously shown that high frequency behavior is influenced by the particular connection used in a capacitor. For a spiral wound tabular capacitor one type of connection is considered, and its equivalent circuit is exhibited. For concentric cylindrical tubular capacitors the only type of connection possible is the one considered for the spiral-wound capacitors. For that configuration a closed form electrostatic induction coefficient and inductance coefficient matrices are presented and used for high frequency analyses

The inductance of the power and ground planes and associated vias is investigated for a high-performance single-chip package. The current distribution in the planes is determined using a novel vector potential. The magnetic intensity in all spatial coordinates due to these currents is determined by the Biot-Savart law. The inductance is proportional to the stored magnetic energy. Special methods for finding the inductance of vias are established. The total inductance is determined. The voltage and ground-plane inductance accounts for less than one quarter of the total, and tab leads and vias are the seat of most of the inductance. To reduce that inductance, shorter, fatter leads can be used, and leads carrying currents in opposite directions should be placed close together to provide as much mutual inductance as possible to cancel self-inductance

The magnetohydrodynamic equations for temporal transients have been formulated and solved for a liquid metal flowing in a rectangular channel with a moving conducting wall and a stationary conducting wall, in the presence of a magnetic field applied normal to the conducting walls. The remaining walls are insulators. It is shown that the transient comprises two exponentially decaying parts: a fast part, believed to be associated with the propagation of Alfven waves, and a slow part, which is the result of viscous and electrical diffusion. Curves of the transients are presented at several stations in the channel

For various reasons, contemporary barrel designs for railguns have tended to be somewhat bulky. Ultimately, the more demanding missions expected of railguns than their conventional chemical counterparts pose a special technical problem for the railgun designer in his attempt to minimize weight and maximize launch efficiency, both of which are crucial in many applications currently contemplated for railguns. The key to achieving the dual goals of weight minimization and efficiency maximization lies in the efficient control of the coupled transient electromagnetic, thermal and mechanical effects against the constraints of realizable material properties. These effects frequently place converse geometric constraints on the design. In a recent design study undertaken by Westinghouse, a barrel concept based on an oval geometry for the barrel cross section and an electromagnetically and structurally shaped geometry for the rails is identified as having the greatest potential in attaining this dual goal, especially for solid-armature driven railguns. To facilitate future design efforts, a design methology is presented which is based on a wide spectrum of computational tools for analyzing the multifaceted barrel performance. The iterations between the design-and-analysis cycles are a crucial interplay for railgun barrel development.

The current and magnetic field distributions in the rails and armature of an electromagnetic launcher are obtained in closed form for the steady state. These solutions assume that the armature moves with a steady velocity and account fully for the two-dimensional skin effect caused by the relative motion between the rails and the armature. Both solid and laminated armatures are considered. It is found in the case of the laminated armature that the phenomenon can be described by a single dimensionless parameter,\\frac{\\ell}{w}\\frac{\\sigma_{o}}{\\sigma_{r}}\\sqrt{\\frac{u\\ell}{\\pi\\eta_{r}}}.

The mathematical model, usage, and documentation of an interactive computer simulation for an electromagnetic launcher is presented. The launcher is modeled as an electrical circuit. Three slight variations of the program permit studies of a launcher with (1) rail skin effects, (2) rail skin effects and approximated storage coil skin effects, or (3) neither of these effects. Usage of the program as currently implemented on the Westinghouse R&D Univac 1106 is described, with a sample session shown. The implementation of the program permits rapid scoping of the effects of parameter changes.

The flux density was measured in a typical tooth of a 500-MV A synchronous generator. Peak flux densities of 14.3, 16.9, and 21.2 kG were observed in an open circuit test at 80%, 100%, and 125% of rated voltage. The search coil voltage waveforms were rich in odd harmonics tending toward a square wave. These voltages were reproduced in an Epstein test frame for the purpose of measuring the core loss in the generator material (M-14), a singly oriented and a cube-textured material. When the turbogenerator tooth flux density waveform was reproduced in the Epstein frame, the measured losses were less than the loss under sinusoidal conditions at all values of induction for all three materials. The less oriented the test material, the greater the relative decrease in losses under the observed tooth flux density wave form. These results are in agreement with an earlier work which established that a square waveform of rate of change of induction produces a minimum core loss.1

Waveforms of the flux densities occurring in the stator and rotor teeth of a 700 hp squirrel cage induction motor were measured for various stator voltage and load conditions. Harmonic analyses were made of these waveforms and the determined harmonic values were compared with the designer's predicted harmonic content. In addition, iron loss measurements determined using the Epstein test method were made on several materials using the same flux variations as existed in the stator and rotor teeth, Losses in the stator teeth were found to be as much as 100% greater, depending on the material being used and the induction level, than the losses measured using a pure 60 Hz sinusoidal flux variation with the same maximum induction. Losses in the rotor teeth were less than 0.1 watt/pound indicating little loss in the rotor teeth (neglecting rotor surfaces losses).

The limiting nonlinear analysis of Sixtus and Tonks is extended to the prediction of the shielding effectiveness of construction steels subjected to electromagnetic pulses. The magnetization curve is approximated by N steps in which magnetic induction or intensity varies but both never vary simultaneously. This method is applied to cylindrical magnetic shields. When applied magnetic intensity exceeds a certain value, a corresponding value of magnetic induction is imagined to form at the surface and propagates inward. As the applied field is increased, successive regions of corresponding magnetization propagate. By the use of Maxwell's curl equations, N simultaneous nonlinear first order differential equations are established and solved to yield the transient distribution of magnetic induction and electrical field intensity.

The limiting nonlinear analysis of Sixtus and Tonks[1] is extended to the prediction of the shielding effectiveness of soft magnetic materials subjected to electromagnetic pulses. The magnetization curve is approximated by N steps in which magnetic induction or intensity varies but both never vary simultaneously. This method is applied to cylindrical magnetic shields. When applied magnetic intensity exceeds a certain value a corresponding value of magnetic induction is imagined to form at the surface and propagates inward. As the applied field is increased successive regions of corresponding magnetization propagate. By the use of Maxwell's curl equations, N simultaneous nonlinear first order differential equations are established and solved to yield the transient distribution of magnetic induction and electric field intensity. An experimental verification of this method is made by discharging a 3 μ f capacitor charged to 30 kilovolts into a 50 Ω triaxial transmission line comprising a 61 cm long middle conductor made of 80% NI-iron and copper inner and outer conductors. The line is matched in its characteristic impedance to minimize ringing. The electric field passing through the thickness of the ferromagnetic tube is monitored by an oxcilloscope separated from the energy source by an iron clad shielded room. The experimentally measured electric fields penetrating the ferromagnetic tube agree with those predicted by the approximate physical model within the bounds of experimental accuracy.