April New Year
In order to explain why the New Year date is in April, we need to understand the solar calendar that was used in that period. A year is divided into 12 Reaseys. Reaseys are the divisions of the path of the Earth around the sun. These Reaseys are Makara Reasey, Khumpheak Reasey, and end with Tnou Reasey. See appendix for a complete list of Reaseys.
These Reaseys correspond to star constellations. Within the twelve Reaseys there is a star called Songkran or Chaitra. This star is selected as a dividing point to end the current year and start a new year. The star divides the Mena and Mesa Reasey. [KHM97] The Earth aligns with the star and the sun in a straight line on April 13 or 14 on the Gregorian calendar in recent years. This marks the day of the New Year.
As soon as the Earth enters Mesa Reasey, it is the first day of New Year called Songkran day. The exact time can be calculated by Horas. By using Dershowitz and Reingold's code, I was able to calculate the date. But the exact time does no coincide with the calculation given in the past by Horas. It differs from ten minutes to over one hour. Consequently, I am not exactly sure how the time is calculated by hora.
Similarly, Laeoung Sak time is the date and time calculated by Horas to determine the ending of the celebration, thus determining if the celebration is 3 or 4 days long. This part of the research needs further investigation. Unfortunately, I do not have enough data to provide more details.
Songkran Time
Below is the list of New Year dates and time collected from different Khmer calendar prints. By comparing to calculations by Dershowitz and Reingold, we can see the time differences ranging from 10 minutes to over an hour.

Table 4: List of Songkran Time in Khmer New Years and Dershowitz and Reingold Songkran Time calculation.
New Data: April 14, 2007 12:48 (actual) -- 13:23(Reingold)
New Data: April 13, 2008 18:28 (actual) -- 19:36(Reingold)
New Data: April 14, 2009 01:36 (actual) -- 01:49(Reingold)
New Data: April 14, 2010 7:36am (actual) -- 08:01(Reingold)
The graph below shows the time differences based on the time of the day that the New Year occurs.

Figure 2: Shows the time differences between Khmer New Year time and calculation using Reingold and Dershowitz calculation.
There seem to be a correlation between the time calculated by Hora and using Reingold's formula. The graph almost appears in a straight line. As the Songkran time approach midnight, the error become minimal.
Songkran Dates
Khmer New Year date is an interesting date. In recent decades, the New Year starts either on April 13 or 14. Below is a list of New Year dates and times generated from the year 1970 to 2020 by using Dershowitz and Reingold's computer code.

Table 5: Reingold and Dershowitz calculation of Songkran date and time from 1970 to 2020.
Looking at different centuries, the New Year can start on dates other than April 13 or 14. This is because the Gregorian calendar is based on seasonal markers that drift clockwise due to the precession of the equinox. The New Year date, however, is determined based on the position of the Earth relative to a star. Thus the same position of Earth relative to a star will fall on different Gregorian dates at different years and centuries.
Below is a list of New Year dates and time based on Reingold's calculation in various centuries.

Table 6: Reingold and Dershowitz calculation of Songkran date and time in various centuries.
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