Calculating the battery runtime

A battery can either be discharged at a low current over a long time or at a high current for only a short duration. Table 1 illustrates the discharge characteristics of a lead acid battery at various loads as expressed in C-rate. At 1C, a 10Ah battery discharges at the nominal rating of 10A in less than one hour. At 0.1C, the same battery discharges at 1A for roughly 10 hours. While the discharge voltage of lead acid decreases in a rounded profile towards the end-of-discharge cut-off, nickel and lithium-based chemistries provide a more steady voltage level through most of the discharge and then drop rapidly at the end of discharge.

Table 1: Typical discharge curves of lead acid as a function of C-rate.

The relationship between the discharge time (in amperes drawn) is reasonably linear on low loads. As the load increases, the discharge time suffers because some battery energy is lost due to internal losses. This results in the battery heating up. The table below indicates the typical discharge time of a 10Ah lead acid battery at various currents.

Discharge current	C-Rate	Discharge time	End of discharge		Table 2: Typical discharge times of a 10Ah lead acid battery as a function of C-rate.
0.5A	0.05C	20h	1.75V/cell
0.1A	0.1C	10h	1.75V/cell
2A	0.2C	5h	1.70V/cell
2.8A	0.28C	3f	1.64V/cell
6A	0.6C	1h	1.55V/cell
10A	1C	0.5h	1.40V/cell

If the battery was a perfect energy source and behaved linearly, a 5A discharge would take two hours to discharge. At a load current of 10A, the same battery would provide energy of one hour. In reality, the relative discharge times are much shorter at higher currents. The losses increase progressively with load. To compensate somewhat, a high current discharge is allowed to terminate at a slightly lower volt per cell, as the forth column of the above table illustrates.

The Peukert number
The efficiently of a battery is expressed in the Peukert number. In essence, the Peukert number reflects the internal resistance of the battery. A value close to 1 indicates a well-performing battery with little losses. A higher number reflects a less efficient battery. The Peukert number of a battery is exponential and checks in between 1.3 and 1.4 for lead acid. The number is lower for nickel-based batteries.

Batteries are stressed the most if discharged at a steady load to the end-of-discharge point. This is the opposite of an internal combustion engine that operates most efficiently with a steady load. On a battery, the intermittent load allows a level of recovery of the very chemical reaction that produces the electrical energy. Because of the rather sluggish behavior, the quiescent rest period is especially important for lead acid. Table 3 illustrates the effective cell capacity of lead acid on a continuous discharge as opposed to an intermitted discharge.

Table 3: The Peukert Curve. The effective cell capacity fades with increased load. An intermittent discharge improves the capacity as it allows the chemical reaction to recover.