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Details of the Mark IV pilot balloon Slide RuleThe slide rule is intended to be used with a Met. Office Pattern Pilot Balloon Theodolite (Watts Mk IIII or V). The divided gradicule of the theodolite along with the scales provided on the slide rule allow for the use of the tail method for estimate the height of the balloon when strong winds are present (elevation angles of 40 degrees of less). Mark V and Mark 5 slide rules were manufactured after this model.
The Mark IV and IV.A were in general use at Meteorological Office stations in the 1960's and 1970's. The Mark IV.A is illustrated below. This model mainly differs from the Mark II in that the stock and sIider, which are 24.5 in (62' 2 cm) long, are made of ivory perspex, or similar plastic material, instead of a wood laminate.
From the Met Office
The general relations used in operating the slide-rule to obtain the height of the balloon h, in feet, the total horizontal distance travelled D, in hundreds of feet, and the easterly and northerly components DE and DN of this distance from the measurements of azimuth A, elevation E and apparent length of the tail m in graticule units are:
where k is the number of graticule divisions per
radian, l the length of the tail in feet, and m its apparent
length in graticule units. Normally the product kl is arranged to be 1.2
X 105. If a different value is used the graticule readings must be
multiplied by 1. 2/kl before calculation on the rule.
In using the slide-rule the normal procedure is first to set the left-hand lower cursor at the observed value of the elevation E on the secant2 scale and to move the slide so that the value of m on the graticule scale is against sec2E. Then, after setting the right-hand lower cursor at the observed elevation on the tangent scale the height is read from the logarithmic scale on the slide. The upper cursors are now set at the observed azimuth on the sine and cosine scales and from these cursors the values of DN and DE are read on the logarithmic scale on the slider. If the value of D is required it can be read from the logarithmic scale opposite sin 90°. Values of the wind components are obtained from the differences of successive values of DN and DE. Then the larger of the components (irrespective of sign) is set at tan 45° on the tangent scale and the reading from this scale against the smaller component gives the angle (less than 45°) between the path of the balloon, in the minute interval concerned, and the nearest of the cardinal lines (W.-E. or S.-N.) bounding the quadrant in question. Finally, with this angle on the sine scale set against the smaller component on the logarithmic scale, the value opposite sin 90° gives the horizontal distance traveled by the balloon in the minute interval, and thus the wind speed in units of 100 ft./min Without further adjustment, the speed may be read off in knots (from the fiducial mark at " K "), in miles per hour (at" Mi/hr ") or in feet per second (at" f/s "). Inter-unit conversions may also be made by direct reading from these fiducial marks. The mark “1•468 " is for conversion from miles per hour to feet per second.
If the observations are made on a moving ship account must
be taken of the ship's course and speed. This is most conveniently done by
adding algebraically the components of the ship's velocity to the components of
the relative wind velocity.
The slide-rule should always be used with care and not
handled with soiled or stained fingers. If it is necessary to clean the surface
warm soapy water should be used. Abrasives, petrol or solvents must never be