Half time (physics)
Encyclopedia
The half time is the time taken by a quantity to reach one half of its final value, where the rate of change is proportional to the difference between the present value and the final value.
The diagram shows the increase in the quantity (red) in response to a step-change in the motive force that changes it (blue). The time-axis is in multiples of the half time. It can be seen that the quantity increases to one-half of its final value after one half time, to three-quarters after two half times, to seven-eighths after three half times, and so on.
The relationship between the quantity (Q) and time (t) is described by the mathematical formula:
where Qf is the final value and is a constant, approximately equal to 0.69 divided by the half time - more precisely: loge(2) / (half time).
Where the quantity decreases in response to a step-decrease in the motive force that changes it, the curve is mirrored in the time-axis and may be referred to as exponential decay.
The concept of half time is used in diving
physiology where body tissues
take up and release inert gases (usually nitrogen
) following changes in depth. Different tissue types have different half times for a given inert gas, and modelling the uptake and release of gases by the tissues is important to avoid decompression sickness
.
The diagram shows the increase in the quantity (red) in response to a step-change in the motive force that changes it (blue). The time-axis is in multiples of the half time. It can be seen that the quantity increases to one-half of its final value after one half time, to three-quarters after two half times, to seven-eighths after three half times, and so on.
The relationship between the quantity (Q) and time (t) is described by the mathematical formula:
where Qf is the final value and is a constant, approximately equal to 0.69 divided by the half time - more precisely: loge(2) / (half time).
Where the quantity decreases in response to a step-decrease in the motive force that changes it, the curve is mirrored in the time-axis and may be referred to as exponential decay.
The concept of half time is used in diving
Scuba diving
Scuba diving is a form of underwater diving in which a diver uses a scuba set to breathe underwater....
physiology where body tissues
Tissue (biology)
Tissue is a cellular organizational level intermediate between cells and a complete organism. A tissue is an ensemble of cells, not necessarily identical, but from the same origin, that together carry out a specific function. These are called tissues because of their identical functioning...
take up and release inert gases (usually nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
) following changes in depth. Different tissue types have different half times for a given inert gas, and modelling the uptake and release of gases by the tissues is important to avoid decompression sickness
Decompression sickness
Decompression sickness describes a condition arising from dissolved gases coming out of solution into bubbles inside the body on depressurization...
.
Examples
- In electronics, when a capacitorCapacitorA capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
is charged or discharged via a resistorResistorA linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
, the voltage on the capacitor follows the above formula, with the half time approximately equal to 0.69 times the time constantTime constantIn physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...
, which is equal to the product of the resistance and the capacitance.
- The first models of nitrogen uptake and release in the body of a diver used five parallel compartments with half times from 5 minutes to 75 minutes. Later models refined this by considering more compartments and a wider range of half times. The U.S. Navy tables used six compartments with half times of 5, 10, 20, 40, 80 and 120 minutes. The Bühlmann tablesBühlmann tablesThe Bühlmann decompression algorithm is a mathematical model of the way in which inert gases enter and leave the body as the ambient pressure changes. It is used to create Bühlmann tables. These are decompression tables which allow divers to plan the depth and duration for dives and show...
use twelve of the sixteen compartments in the ZH-L16 algorithm, which uses half times from 4 to 635 minutes.