How to Calculate Air Resistance of a Falling Object

Whenever objects move relative to the air, the objects experience a resistive force \vec{F_{r}} which is in the opposite direction to the body’s velocity relative to the air. This resistive force is called air resistance. For instance, consider a falling sheet of paper. Relative to the air, the paper is moving downwards, and so there will be an upward resistive force on the paper.

How to Calculate Air Resistance of a Falling Object when the Object Falls Slowly in Air

For objects which move slowly relative to the air (such as falling dust particles), the resistive force is directly proportional to the object’s velocity \vec{v} relative to air. So, we can write:

\vec{F_{r}} = -b\vec{v}

The value of b depends on the shape and size of the body.

Let us consider what happens to a body as it falls from rest at a low speed through the air. Initially, the body’s velocity relative to the air is 0 and so there is no air resistance. As the body speeds up under the resultant downwards force, the air resistance also increases in proportion.Air resistance of a body moving slowly in air

Eventually, the body reaches a speed where the body’s weight is exactly balanced by the air resistance. Here, the body has reached terminal velocityv_{T}. The variation of velocity with time can be shown on a graph, as follows:Air resistance: velocity vs. time graph for a falling body

It can be shown that the terminal velocity for these cases is given by v_{t} = \frac{mg}{b}.


Suppose a pollen grain with a mass of 3.8×10-14 kg is falling through air. If the value of the constant b = 4.0×10-11 kg s-1, find the terminal velocity.

Since v_{t} = \frac{mg}{b},

v_{t} = \frac{3.8\times 10^{-14}\times9.81}{4\times10^{-11}} = 9.3\times10^{-3} \textrm m

Note: In reality, the calculation is not so simple, with many other factors also coming into play. However, for the sake of this example, we have assumed that the only factors which affect the pollen grain’s fall are gravity and air resistance, and the air resistance is also assumed to be directly proportional to the grain’s velocity.

How to Calculate Air Resistance of a Falling Object when the Object Falls Fast in Air

Objects falling faster in the air (for example, skydivers) cause considerable amounts of turbulence, and consequently the air resistance experienced by them is much greater. For these objects, the air resistance is directly proportional to the square of the object’s velocity relative to air. The air resistance for these cases is given by:

F_r = \frac{1}{2}C_{d}\rho Av^2

Here, C_{d} = is drag coefficient, \rho = is the density of air (typically about 1.2 kg m-3), and A = is the effective cross section of the body perpendicular to the direction of the body’s velocity. Typically, C_{d} takes values between 0.1 and 2.

The terminal velocity for objects moving fast in air can be given by v_{t} = \sqrt{\frac{2mg}{C_{d}\rho A}}.


A golf ball falling in air has a drag coefficient of 0.26. Given that it has an effective cross-sectional area of 1.4×10-3 m2, find the air resistance on the ball when the ball is moving at a speed of 20 m s-1.

We have F_r = \frac{1}{2}C_{d}\rho Av^2

Then, F_r = \frac{1}{2} \times 0.26 \times 1.2 \times 1.4 \times 10^{-3}\times 20^2 = 0.087 \textup{ N}

About the Author: Nipun

Related pages

diethyl ether polaritycharacteristics of surrealismadverbs and typeswhat is the difference between ionic and covalent compoundscollective noun for clockssleep apnea narcolepsycontribution in marginal costingsubject verb agreement rule 1 examplesauthorial commentdifference between elevation and altitudehomopolymerizationcompound complex sentence examples for kidsdifference between lime and lemon juicedefine transnational corporationsionizing radiation and nonionizing radiationsnuggle definitionexamples of being facetiouswhat is the difference between a latte and flat whitecharacteristics of formal and informal letterstanza verseformula for calculating angle of reposeleukopenia with neutropeniaconcrete nouns sentencescold and warm blooded animalscalculating arrwhat is the difference between novel and novellatesting for sulphate ionssymbol of pnp and npn transistorfundamental difference between covalent and ionic bondingcystine solubilitydifference between seal and sea lionpurpose of the prologueexamples of enjambment in poetrywhat is the difference in a typhoon and a hurricanenegative reinforcement definition psychologydifference between alligator and crocodilesimilarities between comedy and tragedyclass and caste system definitionhamartia meanssynecdoche metonymydifference between bulimia and bulimia nervosacliche idiomsahmedabad cotton textile industryplasma oncotic pressure definitioninelastic collision vs elasticdifference between covalent ionic and hydrogen bondswhat is the difference between hypertonic solution and hypotonic solutionwhat is one difference between primary and secondary successiondifferences between osmosis and diffusionmoral of the story the ant and the grasshopperpatronize examplewhat is the difference between anorexia nervosa and bulimia nervosatypes of essay formatsamicabledefinitionaffectionate definecytosine and thymine arehoratiancanoe and kayak differencewhat is the difference between prose and dramacad chdwhat is archebacteriacompare the structure of monosaccharides disaccharides and polysaccharidesdifference between polarized and unpolarized lighthow does renaissance art differ from medieval artthe moral of cinderellamicrometer and calipercolloid solution definitionpredicate nomativebiscuit cookie differencetest for sulfatesdistinguish between n-type and p-type semiconductorprepositions and conjunctionshyperglycemia hypoglycemiatypes of agnosticsidioms and proverbshow to subtract vectors in physicselk compared to moose