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Calculate water heater recovery
Water heater recovery is used to calculate first hour delivery: Calculate first hour
Recovery Capacity
... is the maximum amount of water that can be heated by a water heater with a given temperature rise in one hour.
Recovery is typically measured in gallons per hour (GPH).
Generally, more BTUs or higher wattage input means faster recovery rate. 
Recovery rates are also a component of the First Hour Rating which is basis for water heater sizing. Resource: How to calculate first hour
GPH gallon per hour recovery for ELECTRIC water heater
= Watts divided by [2.42 x temperature rise in F]
Requirements:
You need incoming water temperature and actual temperature of water inside tank.
Note: thermostat calibration is approximate so actual temperature of water inside tank is unknown without measuring.
Install temperature gauge
Buy: temperature-pressure gauge
Winters Temperature gauge
Note: Seasonal fluctuations in local incoming water temperature vary year-round.
Other variables such as efficiency are not considered in the formula.
Resources:
Water heater formulas .pdf
Ways to increase amount of hot water
Recovery calculations for Electric water heater/ summer and winter:

A) Typical residential non-simultaneous water heater with 4500 watt elements.
Summer: 65 incoming water temperature. Resource: Average temperature shallow ground water
Thermostat set to 125F:
4500 watt divided by [2.42 x 60 rise in temperature] = 31 GPH summer
Winter: 40 incoming water temperature.
Thermostat set to 125F:
4500 watt divided by [2.42 x 85 rise in temperature] = 21 GPH winter

B) Residential water heater converted to simultaneous wiring
Install 2 - 5550 watt elements each connected to a separate 30 amp breaker. Resource: How to wire simultaneous water heater
Summer: 65 incoming water temperature.
Thermostat set to 125F. Resource: How to adjust water heater temperature
11000 watts divided by [2.42 x 60 rise in temperature] = 75 GPH summer
Winter: 40 incoming water temperature.
Thermostat set to 125F:
11000 watt divided by [2.42 x 85 rise in temperature] = 53 GPH winter

Increase recovery by raising thermostat
Raise recovery by changing thermostat setting. Resource: How to adjust water heater temperature
Upper and lower thermostat can be set differently.
A timer can be used to control temperature differences, and save money by toggling the water heating capacity depending on peak usage times. Resource: Use timer to control thermostats
 

Increase recovery by installing tempering tank to passively preheat incoming cold water
Tempering tank

Increase recovery by installing 2 water heaters
2 water heaters mean higher volume of hot water is available, and user is less likely to run short of hot water
Resource: Two water heaters

Opinion:
Raising thermostat to 130F is easiest way to increase recovery. Installing tempering tank is extra work but affective for cold incoming water.

If very high recovery is needed, then wiring extra breaker and running another 10 gauge wire for simultaneous operation is best way to increase recovery.
Resource:   How to wire simultaneous water heater
Converting to simultaneous is more work, but safer than increasing water temperature to 140-150F.
Temperature gauge
Permanent install on hot pipe leaving water heater.

Buy:
Winters Temperature gauge
Temperature-pressure gauge for boiler
GPH gallon per hour recovery for Gas water heater
= BTUs per hour divided by [11.0 x temperature rise in F]
GPH gallon per hour recovery for GAS water heater =
BTUs per hour divided by [11.0 x temperature rise in F]

To accurately calculate temperature rise, you need incoming water temperature and actual temperature setting
Note: thermostat calibration is approximate and actual temperature of hot water is not known without measuring.
Note: Seasonal fluctuations in local incoming water temperature vary year-round.
Other variables such as efficiency are not considered in the formula.
Gas water heaters recover faster than electric.
Resource:s
Water heater formulas .pdf
Water heater efficiency calculation
Ways to increase amount of hot water
Recovery calculations for Gas water heater/ summer and winter:

A) 30 gallon gas heater with 40,000 BTU heater
Summer: 65 incoming water temperature.
Thermostat set to 125F.
40,000 BTU divided by [11 x 60 rise in temperature] = 60 GPH summer.

B) 40 gallon gas heater with 40,000 BTU heater
Winter: 40 incoming water temperature.
Thermostat set to 125F.
40,000 BTU divided by [11 x 85 rise in temperature] = 42 GPH winter.
Problems with setting thermostat too high:
Very hot water poses extreme risk of scalding. 140-150F is extremely dangerous
Hotter water heater temperatures increase pressures inside the tank, shortening life of tank that is rusted. Prevent tank from rusting
Very hot water can cause leaks or drizzling TP valve.
A tank that is connected to pipes in a closed system where expansion of water is confined by a check valve or pressure-reducing valve, can experience damaging/dangerous pressure increases when thermostat temperatures are set very high.
Resources:
Closed system .pdf
Install pressure tank to prevent closed system
Very hot water poses risk of scalding.
Temperatures above 135 are extremely dangerous and will scald the skin in seconds.
Average bath-shower temperatures are 104-110 and rarely much higher.
120 F thermostat setting is considered best for optimal savings, 140F is for killing bacteria .

Hotter water heater temperatures increase pressures inside the tank, possibly shortening life-span of tank, causing rupture or drizzling TP valve.
Prevent rusted tank by replacing anode rod:
Resource: How to replace anode rod

A tank that is connected to pipes in a closed system where expansion of water is confined by a check valve or pressure-reducing valve, can experience dangerous pressure increases when thermostat temperatures are set very high.
Resource: Prevent damage from closed system

Additional links

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