When the fast came too fast
How a 40-minute delay brought in Taanis Esther 5 hours early
Please note: The numbers in this article are approximate and intended for illustration purposes only.
Travelers from Tel Aviv to New York on the morning of Taanis Esther 5774 were informed by MyZmanim
Air™ inFlight Zmanim that if the flight departs at 1:00 AM the fast begins at 10:25 AM, but if it departs at
1:40 AM the fast begins at 5:40 AM. Many wondered: Why would a delay in the time of takeoff cause
the fast begin earlier? Also, how could a delay of only 40 minutes account for a 5 hour change in when
the fast begins? In the following article we will explain why this is so.
Imagine that Reuven and Shimon are running in a marathon. Shimon runs 15 MPH (miles per hour) but
Reuven runs only 9 MPH. Reuven is given a head-start and begins the marathon 32 miles ahead ofShimon.

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When the fast came too fast

Using the graphs in Figure #1, you can check the distance covered by Reuven and Shimon at any
moment. The moment at which Shimon passes Reuven is indicated by the point where the lines
intersect.
For example, you can see that if Reuven begins running “on time” at 1:00 AM (the graph on the left)then by 4:00 AM he will have covered a total distance of about 60 miles (32 + 27 = 59). If Reuven begins
running “40 minutes late” at 1:40 AM (the graph on the right) then by 7:00 AM he will have covered atotal distance of 80 miles (32 + 48 = 80). Either way, by 1:00 PM Shimon will have run 180 miles (15 MPH
x 12 hours).
Notice that when both begin running at 1:00 AM, Shimon passes Reuven at 6:20 AM. But when Reuven
begins 40 minutes late, he is overtaken by Shimon at 5:22 AM.

Figure #1
On time40 minutes late

200200180180160160140140120

120

100

100

80

80

6060

40

40

20

20

00
1:00

4:00

7:00

10:00

Shimon

13:00

16:00

1:00

Reuven

4:00

7:00
Shimon

10:00

13:00

16:00

ReuvenBoth begin running at 1:00 AM. Shimon passes Reuvenat 6:20 AM.

Shimon begins at 1:00 AM, Reuven begins at 1:40 AM.
Shimon passes Reuven at 5:22 AM.

On time40 minutes lateTimespan
Head start
1:00 to 6:20
TOTAL

Hours
05.3̅

Miles
Miles
covered bycovered by
ReuvenShimon(9 MPH)(15 MPH)
32048
80
80
=80

Timespan Hours
Head start00.6̅
1:00 to 1:40
1:40 to 5:22
3.7
TOTAL

2

Miles
Miles
covered bycovered by
ReuvenShimon(9 MPH)(15 MPH)32
00
10~33.5
55.5
65.5
=65.5

When the fast came too fast
Now suppose, after running for 4.5 hours, Reuven gets a burst of adrenaline and is now running as fastas Shimon (15 MPH). 4 hours later, Reuven is no longer able to sustain this pace and slows back down tohis initial 9 MPH. The graphs in Figure #2 show that when they both start running at 1:00 AM Shimon
passes Reuven at 10:18 AM. But when Reuven starts running 40 minutes late at 1:40 AM, he isovertaken by Shimon at 5:18 AM. Because Reuven began a mere 40 minutes late, he will be overtaken 5hours earlier!

Figure #2On time

40 minutes late

200

200

180

180

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20

00
1:00

4:00

7:00

10:00

Shimon

13:00

16:00

1:00

Reuven

7:00
ShimonBoth begin the marathon at 1:00 AM. Shimon passes
Reuven at 10:18 AM.

10:00

13:00

16:00

ReuvenShimon begins at 1:00 AM, Reuven begins at 1:40 AM.
Shimon passes Reuven at 5:18 AM.

On timeTimespan Hours
Head start
1:00 to 5:30
4.5
5:30 to 9:30
4.0
9:30 to 10:18
0.8
TOTAL

4:00

40 minutes late

Miles
Miles
covered bycovered by
ReuvenShimon(9,15,9)(15 MPH)
32
0
40.5
67.5
60
60
~712139.5 = 139.5

Timespan Hours
Head start
0.6̅
1:00 to 1:40
1:40 to 5:18 3.63̅
TOTAL

Miles
Miles
covered bycovered byReuven
Shimon(9,15,9)(15 MPH)32
00
10~32.5
54.5
64.5
=64.5

Keeping all numbers the same, let’s replace Reuven and Shimon with an aircraft and the zman of Alos
Hashachar, respectively. Alos Hashachar is “running” westbound at a rate of 15 degrees of longitude perhour. The aircraft is also traveling westbound, but at varying rates. During the beginning segment of theflight, the aircraft travels at a rate of 9° / hr (ie. 9 degrees of longitude per hour). During the middle
segment its rate is 15° / hr, and during the final segment its rate returns to 9° / hr. The aircraft is given a3

When the fast came too fast“head start” by virtue of the fact that it departs from Tel Aviv which is geographically located 32 degrees“ahead” of the place where Alos Hashachar occurs at 1:00 AM.
The moment at which Alos Hashachar “passes” the aircraft is when the fast begins for the passengers.
Hence, if the takeoff is at 1:00 AM, the fast begins 10:18 AM. But if the flight is delayed 40 minutes, thefast begins 5:18 AM.
Finally, we must account for the fact that the change in travel rate occurs gradually rather than abruptly.
The graphs in Figure #3 are based on actual data which MyZmanim™ collected for an arbitrary El Alflight. These graphs allow you to check the current longitude position of Alos Hashachar and our aircraft
for any moment. For example, we can see that if takeoff was delayed 40 minutes, at 10:00 AM theaircraft will be at longitude -50°. In this figure, the first and final segments of the trip appear curved
rather than straight. This reflects the reality that the aircraft travel rate transitions gradually from 9° / hrto 15° / hr and back to 9° / hr.
Also depicted is the fact that the fast beginsa at 10:25 AM if takeoff is on time, and at 5:40 AM if takeoff
is delayed 40 minutes.

Figure #3
On time40 minutes late

-110

-110

-90

-90

-70

-70

-50

-50

-30
-10 1:00

-30
4:00

7:00

10:00

13:00

16:00

-10 1:00

101030

30

50

50

70

70

90

90
Alos

Aircraft

4:00

7:00

Alos

Takeoff is on time. Fast begins at 10:25 AM.

10:00

13:00

16:00

AircraftTakeoff is delayed 40 minutes. Fast begins at 5:40 AM.

4When the fast came too fast
You may be wondering: If the aircraft cruise speed remains a constant 600 MPH throughout its journey,
why does its degrees-per-hour rate vary?
The answer lies in the fact that the aircraft’s direction of travel varies throughout the journey. Lines oflongitude are crossed only when traveling east and west but not when traveling north and south.
Therefore, the same 600 miles covered each hour represents a greater longitude distance whentraveling directly West (during the middle segment of the trip) than when traveling North-West andSouth-West (during the first and final segments of the trip).
Copyright © June 2014 by R’ Dovid Eisikowitz

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