Positioning a photovoltaic (PV) array in the optimal orientation increases the collection of solar radiation and the production of electricity. Many methods for determining the optimal tilt angle of a fixed PV array have been reported in the literature; however, few methods have been proposed for finding the optimal tilt angle of a 2-axis time-position tracking PV array. This paper derives and validates a simple formula for directly calculating the optimal tilt angle of a 2-axis time-position tracking PV array under varying sky conditions. By modifying the conventional tilt angle as the sky conditions change, the tracking PV array can glean the additional small amounts of irradiance that are overlooked and unused on cloudy days. The validity of this formula was verified using 24 months of weather data from an installation in the northeastern United States where clear skies occur about 39% of the time. Simulations indicated that modifying the conventional 2-axis tracking angles in response to changing cloud cover results in 2.3% increase in collected insolation and 2.4% increase in AC energy over a 24-month period. During hourly and sub hourly intervals with cloud cover, the increase in energy collection can reach up to 50%. The ability to modify the conventional tracking angles in response to changing cloud cover allows the PV array to glean the previously uncollected energy, thereby capturing more of the total available irradiance and increasing electrical power production. (C) 2017 Elsevier Ltd. All rights reserved.