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1995,  Table I  -  Page 3 Driving along a road in Argonia, Kansas;  September 1, 16 1995; Co-ordinates  = 37°40'00"N, 97°00'00"W;  Altitude (approx.)= 412 msl;   Magnetic Declination = 6.6°E (Add 6.6° for True);  Magnetic Inclination = 66.6°;   Observer:  Robert D. Stephens

Obs.

Species

Date (Time)

Flight Behavior

Weather

Field Notes

I

II

III

IV

Va

Vb

Part 1

Part 2

Part 3

Obs.  Alt.*

Type of Flt.

Horiz. Path

Vert. Path

Mag. Bear.

Mag. Head.

Wind Dir.

Wind  Vel.

Amb. Temp.

Thrm. Act.

Cloud  Types

1

Danaus plexippus

Sept. 24

0.3 - approx. 2 m

flap

straight

level (approx.)

S

-

S

-

-

-

none

-

*Observed altitude above the ground. Data was recorded in a Pilots Log.  On Sept. 24  day Robert Stephens observed 32 - 40 crossing the road for mile after mile. He also wrote that at at 4000 ft above the ground, he has had the following come through the air vent: air at 26 F (C), air at 104 F (C),  grasshopper, other insects, wheat straw, Milo grain, Milo leaves, dirt, rain, fog, misc. junk, and U.F.O.'s.  No butterflies. Comments by Gibo:    He provided a page of useful calculations showing how to estimate the density of migrating Monarchs (or other butterflies) in a region from numbers observed crossing the road while driving.   Robert Stephens' method, discussed below, although similar to the method used by Dick Walton at the Cape May Bird Observatory New Jersey, differs in significant details.

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Calculations

Robert Stephens Method of Estimating Numbers of  Migrating Butterflies.
The method is an index and involves driving along a road at a constant speed while counting butterflies.  In his example, he was driving on an East/West road,   perhaps Highway 160, when he observed mile after mile of migrating Monarch butterflies crossing perpendicular to the road at about 1 ft to the top of  his windshield.    As he drove a measured distance, one mile ( 5,280 ft. or 1, 609.3 m) in a measured time,  one minute, he counted the butterflies that crossed the white center line.  He did not count butterflies that were either approaching the center line, or had already flown pass the line when he spotted them.  His counts ranged from 32 to 40 per mile with an average of 35 per mile (21.7 per km).   This result can be used to calculate a rough estimate of density of  35 x 35 = 1,225  per square mile (471 per square km).   Robert Stephens pointed out in his letter, however,  that the actual sample was longer then a mile because you have to account for the speed of butterflies as they flew across the road.   The actual distance is the hypotenuse of the right triangle with one side having a length of   1,609.3 m, and the other side the distance that the butterflies can fly in one minute.  As it turns out, this is not a serious concern for a census taken at highway speeds (see below).  

Estimating Numbers of Migrating Monarch Butterflies from a Moving Vehicle.
Assuming that: (1) the butterflies are flying perpendicular to the road,  (2) they are flying into a headwind,  and (3) they are flying at their cursing airspeed of 5 m/s,  or 60 x 5 = 300 m/min.   Because 5 m/s is the maximum ground speed that the butterflies can achieve if they are flying close enough to the ground to avoid (duck under) the headwind,  then the actual length of the one minute transect through the migrating population is the square root  of sum of the squares of the two sides.   In Robert Stephens' sample, the length of the hypotenuse is 1637.0 m.  This distance is only  1.7 % longer than the measured distance.   To correct for the error,  we multiply 35 by (1.0 -0.017).  The correct sample size is  35 x 0.983 = 34.4 per mile (21.4 per km).  The corrected population density is 1,183.4 per square mile (458 per square km).  It is important to keep in mind that this estimate assume that the butterflies were avoiding the head wind and flying at their cruising airspeed.   Because monarch butterflies are unlikely to be completely successful in avoid the headwind,  then they were probably making slower progress and the population estimate is inflated.  Nevertheless, the error is small and true number of butterflies crossing each mile of highway per minute was between 35.0   to 34.4 per mile (21.4 to 21.7 per km).   Error increases for slower highway speeds unless the hypotenuse method is used.  The following tables provide the correction factor for a range of highway speeds.

[this section is still under construction]

Example 1:  Seventeen monarch butterflies are counted crossing the center line during a one minute sample.  Vehicle speed was 20 mph.  The corrected count is 0.873 x 17 = 14.8 butterflies per mile per minute.  The density of the migrating population is 14.8 x 14.8 = 219.0  butterflies per square mile.   

Example2:  Seventeen monarch butterflies are counted crossing the center line during a one minute sample.  Vehicle speed was 35 mph.  The corrected count is 0.953 x 17 = 16.2 butterflies per mile per minute.  The density of the migrating population is 16.2 x 16.2 = 262.4 per square mile.  

Example 3:  Seventeen monarch butterflies are counted crossing the center line during a one minute sample.  Vehicle speed was 30 km/hr.  The corrected count is 0.857 x 17 = 14.6  butterflies per km per minute.  The density of the migrating population is 14.6.2 x 14.6 = 213.2 per square km.  

Example 4:  Seventeen monarch butterflies are counted crossing the center line during a one minute sample.  Vehicle speed was 55 km/hr.  The corrected count is 0.950 x 17 = 16.2 butterflies per km  per minute.  The density of the migrating population is 16.2 x 16.2 = 262.4 per square km.