The most efficient tilt for photovoltaic panels in Kansas City, Missouri at a latitude of 39.12°:
Your photovoltaic panels need to be angled facing south.
If you're mounting the photovoltaic panels at a stationary angle, such as on your roof, the most efficient angle is 32.8°.
If you're planning to change the angle of your photovoltaic panels twice per year, the most efficient angle is 15.4° in summer months and 53.4° in winter months.
If you're planning to change the angle of your photovoltaic panels each season, the most efficient angle is 11.7° in summer months and 58.8° in winter months, and 36° in autumn and spring months.