Slant Length Research Articles

Radar and Seismic Ice-Thickness Measurements Compared on Sub Polar Glaciers in Svalbard (Abstract)

A comparison has been made of 46 radar-determined ice thicknesses and those resulting from seismic sounding on Bakaninbreen, Skobreen, and Paulabreen in central Spitsbergen. Significant differences were recorded between the two techniques, with 50% of the comparisons exceeding 15 m. Systematic differences between the three glaciers were also observed: on Paulabreen the seismic ice depths are consistently deeper than those determined by radio echo- sounding, whilst the opposite is true on Skobreen. Instrumental errors from the radar (SPRI 60 MHz unit) and seismic equipment (ABEM Terraloc) are considered small or insignificant. Factors affecting the respective propagation velocities may be responsible for differences in mean thickness particularly in the case of seismic waves, although the changes are obtained from the first returns. One hypothesis to explain the differences on Paulabreen, and to a lesser degree on Bakaninbreen, is that these glaciers are underlain by a seismic low-velocity layer due to the presence of moraine or till. Unfortunately, equipment problems in the field prevented the digital logging of the seismic data and the analogue records are not of sufficient quality for detailed analyses to reveal the possible presence of a till horizon and its seismic velocities. However, observations at the snout of Paulabreen show considerable thicknesses of basal till. With a “P”-wave velocity in such a layer close to or less than that of ice acoustic returns would possibly come from the till–bedrock interface, whereas radar returns would be from the region of the ice–till boundary. For the seismic ice depths that are shallower than the radar soundings on Skobreen an alternative explanation is required. The valley occupied by the glacier is considerably narrower than in the case of the other two glaciers. According to one detailed radio echo-sounding cross-profile, the line of the combined seismic and radar sounding was displaced to one side of the centre and deepest part of the glacier. This would result in early seismic returns from the nearest facets of the valley side rather than the subjacent bed. The radio waves, however, undergo a focussing effect in the ice, giving rise to a considerably smaller footprint. The difference in slant length between the general area of the bed viewed by the radar and that returning seismic energy is approximately +15–20 m at the location of the cross-profile. This value is of the order of the differences between the two systems and could therefore account for the observed disparity here and at the other locations.

Radar and Seismic Ice-Thickness Measurements Compared on Sub Polar Glaciers in Svalbard (Abstract)

A comparison has been made of 46 radar-determined ice thicknesses and those resulting from seismic sounding on Bakaninbreen, Skobreen, and Paulabreen in central Spitsbergen. Significant differences were recorded between the two techniques, with 50% of the comparisons exceeding 15 m. Systematic differences between the three glaciers were also observed: on Paulabreen the seismic ice depths are consistently deeper than those determined by radio echo- sounding, whilst the opposite is true on Skobreen.Instrumental errors from the radar (SPRI 60 MHz unit) and seismic equipment (ABEM Terraloc) are considered small or insignificant. Factors affecting the respective propagation velocities may be responsible for differences in mean thickness particularly in the case of seismic waves, although the changes are obtained from the first returns. One hypothesis to explain the differences on Paulabreen, and to a lesser degree on Bakaninbreen, is that these glaciers are underlain by a seismic low-velocity layer due to the presence of moraine or till. Unfortunately, equipment problems in the field prevented the digital logging of the seismic data and the analogue records are not of sufficient quality for detailed analyses to reveal the possible presence of a till horizon and its seismic velocities. However, observations at the snout of Paulabreen show considerable thicknesses of basal till. With a “P”-wave velocity in such a layer close to or less than that of ice acoustic returns would possibly come from the till–bedrock interface, whereas radar returns would be from the region of the ice–till boundary.For the seismic ice depths that are shallower than the radar soundings on Skobreen an alternative explanation is required. The valley occupied by the glacier is considerably narrower than in the case of the other two glaciers. According to one detailed radio echo-sounding cross-profile, the line of the combined seismic and radar sounding was displaced to one side of the centre and deepest part of the glacier. This would result in early seismic returns from the nearest facets of the valley side rather than the subjacent bed. The radio waves, however, undergo a focussing effect in the ice, giving rise to a considerably smaller footprint. The difference in slant length between the general area of the bed viewed by the radar and that returning seismic energy is approximately +15–20 m at the location of the cross-profile. This value is of the order of the differences between the two systems and could therefore account for the observed disparity here and at the other locations.

Non-linear free vibrations of conical shells

The non-linear characteristics of free vibrations of conical shells, including both circular cylinders and annular plates as special cases, have been investigated. Donnell type theory was utilized to prescribe the shells and the trial functions of the assumed mode were obtained by means of the finite element method. The method of weighted residuals applied to time variables furnished the non-linear algebraic equations to be solved for the dependency of the frequency upon the amplitude. Comparisons of the results with those obtained in previous investigations were made for a cylinder and for an annular plate. The numerical results elucidated the characteristics of the softening type of vibrations of conical shells with fixed edges which have a ratio of slant length to the small radius of 1·6125 and a ratio of thickness to the small radius of 1·25 × 10 −3.

円錐殻の超音速パネルフラッタ(第II報)風胴実験

Unstiffened truncated conical shells were tested for flutter at a Mach number 2.0 in the NAL 1-by 1-meter blowdown wind tunnel. The shells were made of super-invar in order to avoid the thermal stresses and had a ratio of slant length to small radius 1.61 and a semivertex angle of 14°. The experimental results were in good agreement with a flutter boundary calculated by the FEM based on a Donnell-type theory. Vibration and external pressure buckling tests were also performed with good agreement be- tween theory and experiment.

Stability of internally pressurized conical shells under torsion

E = modulus of elasticity h — thickness of shell I = slant length of cone n = number of circumferential waves p = internal hydrostatic pressure pe = critical external hydrostatic pressure denned by Eq. (2) Ri = radius of small end of truncated cone R2 = radius of large end of truncated cone T = torque Z = curvature parameter for cylinder (1 — )/(L a. = semivertex angle of the cone v = Poisson's ratio pav = mean radius of curvature = (Ri + Rz)/2 cos a T = maximum torsional stress = (T/2wRih) Tcr = critical torsional stress given by Eq. (1)

Experiments on Cone Drag in a Rarefied Air Flow

Experiments were made to find the drag on the fore portion of a circular cone in a rarefied supersonic flow. Wind-tunnel tests on a cone of 15 deg half angle were conducted over a range of Reynolds number (based on freestream properties and cone slant length) of 70 to 1500 at Mach 2 and 500 to 7000 at Mach 4. The experimental drag curves are in fair agreement wi th available boundary layer predictions if certain induced pressure and tranverse curvature effects are included, a l though some difference in trend of the experimental and theoretical curves is evident.