What Is Drag?

Drag is a resistive force that acts on an object moving through a fluid.

A fluid is a substance that can flow. Both liquids and gases are fluids, so drag can occur when objects move through:

• air
• water
• oil
• other liquids
• other gases

When an object moves through a fluid, drag generally acts in the direction opposite to the object's motion relative to the fluid.

For an object falling through still air:

↓ Motion

↑ Drag

↓ Weight

For a car moving forward through still air:

Car →

← Air resistance

Air resistance is a type of drag force.

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What Causes Drag?

As an object moves through a fluid, it interacts with the particles of that fluid.

The object must push fluid particles out of the way. The fluid also exerts forces on the object's surface.

These interactions produce a force that resists the object's motion.

Drag is therefore caused by interactions between the moving object and the surrounding fluid.

Unlike ordinary friction between two solid surfaces, drag occurs when an object moves relative to a liquid or gas.

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Direction of Drag

Drag acts opposite to the relative motion between an object and the fluid.

If an object falls downward through still air:

Drag acts upward.

If an object rises upward through water:

Drag acts downward.

If a cyclist moves forward through still air:

Drag acts backward.

This is similar to friction: drag resists relative motion.

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Drag Depends on Speed

One of the most important factors affecting drag is speed.

Generally:

Greater speed → greater drag

When an object moves slowly through a fluid, it interacts with relatively little fluid each second.

When it moves faster, it must push more fluid out of the way each second, and the interactions become stronger.

Therefore, drag increases.

For many objects moving through air at moderate or high speeds, drag can be approximately related to the square of speed:

Fd ∝ v²

This means that doubling speed can produce roughly four times as much drag under conditions where this model applies.

However, the exact relationship between drag and speed depends on the situation and the way the fluid flows around the object.

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A Common Drag Equation

For many objects moving through fluids, drag can be modeled using:

Fd = ½ρCdAv²

where:

• Fd = drag force (N)
• ρ = density of the fluid (kg/m³)
• Cd = drag coefficient
• A = cross-sectional area (m²)
• v = speed relative to the fluid (m/s)

You do not always need to calculate drag using this equation, but it reveals the main factors affecting it.

Drag depends on:

fluid density, shape, area, and speed.

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Cross-Sectional Area

The cross-sectional area is the area of an object facing the flow of the fluid.

A larger area usually produces more drag.

Compare a skydiver in two positions.

A skydiver with arms and legs spread out presents a large area to the airflow.

Larger area → greater drag

A skydiver with the body tucked into a streamlined position presents a smaller area.

Smaller area → less drag

This allows skydivers to control their falling speed by changing body position.

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Shape and Drag

The shape of an object strongly influences drag.

A streamlined shape allows fluid to flow around an object more smoothly.

This usually reduces drag.

Streamlining is important in the design of:

• aircraft
• cars
• racing bicycles
• trains
• submarines
• boats
• swimming equipment

Engineers try to reduce unnecessary drag because drag can decrease speed and increase energy consumption.

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Fluid Density

Drag also depends on the density of the fluid.

Generally:

Greater fluid density → greater drag

Water is much denser than air, so moving quickly through water usually produces much greater resistance than moving at the same speed through air.

You can experience this easily by moving your hand quickly through water compared with moving it through air.

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Falling Objects

Drag becomes particularly important when analyzing objects falling through the atmosphere.

Imagine dropping an object from a large height.

Two important forces act on it:

↑ Drag

●

↓ Weight

Weight is:

Fg = mg

Immediately after release, the object has almost no speed.

Therefore, drag is initially very small.

Weight is much greater than drag.

So:

Fnet downward > 0

and the object accelerates downward.

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Stage 1: Beginning to Fall

At the moment the object is released:

Speed ≈ 0

Therefore:

Drag ≈ 0

Weight acts downward:

↓ Fg

The object experiences a large downward resultant force.

Using Newton's Second Law:

Fnet = ma

the object accelerates downward.

Its speed begins to increase.

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Stage 2: Speed Increases

As the object falls faster:

Speed increases → drag increases

Weight remains approximately constant, but drag becomes larger.

For example:

↑ Drag = 200 N

●

↓ Weight = 700 N

The net force is:

Fnet = 700 − 200

Fnet = 500 N downward

The object is still accelerating downward.

However, because the net force has become smaller, its acceleration is also smaller.

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Stage 3: Drag Continues to Increase

As speed continues increasing, drag continues increasing.

Eventually:

↑ Drag = 500 N

●

↓ Weight = 700 N

Net force:

Fnet = 200 N downward

The object is still speeding up, but its acceleration is becoming smaller.

This process continues until drag equals weight.

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Terminal Velocity

Eventually, the drag force becomes equal in magnitude to the object's weight.

↑ Drag

●

↓ Weight

When:

Fd = Fg

the forces are balanced.

Therefore:

Fnet = 0

From Newton's Second Law:

Fnet = ma

so:

a = 0

The object stops accelerating.

However, it does not stop moving.

Instead, it continues falling at a constant velocity.

This constant falling velocity is called terminal velocity.

Terminal velocity is the constant velocity reached when the resultant force on a moving object becomes zero because the forces acting on it are balanced.

For a falling object:

Drag = Weight

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Terminal Velocity Does Not Mean Zero Velocity

This is one of the most common misunderstandings.

At terminal velocity:

velocity ≠ 0

Instead:

acceleration = 0

The object continues moving at a constant velocity.

Newton's First Law tells us that an object with zero resultant force continues moving at constant velocity.

Therefore:

Fnet = 0 does not mean v = 0.

It means:

a = 0.

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Velocity-Time Graph for a Falling Object

The motion of a falling object approaching terminal velocity can be represented using a velocity-time graph.

At first, velocity increases rapidly.

As drag increases, acceleration decreases.

The graph gradually becomes less steep.

Eventually the graph becomes horizontal.

A horizontal section means:

constant velocity

Therefore:

acceleration = 0

This horizontal velocity represents terminal velocity.

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Acceleration During the Fall

Remember that the gradient of a velocity-time graph represents acceleration.

At the beginning:

large gradient → large acceleration

Later:

smaller gradient → smaller acceleration

At terminal velocity:

gradient = 0 → acceleration = 0

This connects drag forces directly to motion graphs.

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Skydiving and Terminal Velocity

Skydiving provides a useful example of terminal velocity.

When the skydiver first jumps:

Weight > Drag

The skydiver accelerates downward.

As speed increases:

Drag increases

Eventually:

Drag = Weight

The skydiver reaches terminal velocity.

The skydiver continues falling at a constant speed.

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What Happens When the Parachute Opens?

When the parachute opens, the skydiver's cross-sectional area increases dramatically.

Therefore:

Area increases → drag increases

Immediately after the parachute opens:

Drag > Weight

The net force is now upward.

Because the skydiver is still moving downward but has an upward acceleration, the skydiver slows down.

As the downward speed decreases, drag decreases.

Eventually:

Drag = Weight again

The skydiver reaches a new terminal velocity.

This second terminal velocity is much lower because the open parachute produces much more drag at a given speed.

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Terminal Velocity and a Parachute

We can summarize the process:

Before parachute opens

Small area → less drag → higher terminal velocity

After parachute opens

Large area → more drag → lower terminal velocity

The parachute does not remove gravity.

Instead, it increases drag enough that the skydiver reaches a much lower terminal velocity.

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Factors Affecting Terminal Velocity

Terminal velocity depends on several factors.

1. Mass and Weight

A larger mass produces a larger gravitational force:

Fg = mg

A larger drag force is therefore required to balance the weight.

Because drag increases with speed, a heavier object with otherwise identical shape and area generally needs to fall faster before drag becomes large enough to balance its weight.

Therefore, under otherwise identical conditions:

Greater mass → higher terminal velocity

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2. Cross-Sectional Area

A larger area creates greater drag at a given speed.

Therefore:

Larger area → lower terminal velocity

This is the principle behind parachutes.

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3. Shape

More streamlined objects generally experience less drag.

Therefore:

More streamlined shape → potentially higher terminal velocity

A broad or less streamlined object usually experiences greater drag and reaches a lower terminal velocity under otherwise similar conditions.

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4. Fluid Density

Denser fluids produce greater drag at the same speed.

Therefore:

Greater fluid density → lower terminal velocity, all else being equal.

This is one reason objects behave differently when falling through water compared with falling through air.

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Estimating Terminal Velocity

If drag is modeled by:

Fd = ½ρCdAv²

then at terminal velocity:

Fd = mg

Therefore:

mg = ½ρCdAvt²

Rearranging:

vt = √(2mg / ρCdA)

This equation shows clearly how different factors affect terminal velocity.

Increasing m tends to increase terminal velocity.

Increasing ρ, Cd, or A tends to decrease terminal velocity.

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Worked Example 1: Identifying Terminal Velocity

A falling object has a weight of 500 N. At a particular speed, the drag force is 500 N upward.

What happens to the object?

Weight = 500 N downward

Drag = 500 N upward

Therefore:

Fnet = 500 − 500

Fnet = 0 N

So:

a = 0 m/s²

The object continues falling at constant velocity.

It has reached terminal velocity.

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Worked Example 2: Calculating the Net Force

A skydiver has a weight of 750 N. The upward drag force is currently 450 N.

Calculate the net force.

Fnet = Weight − Drag

Fnet = 750 − 450

Fnet = 300 N downward

The skydiver is therefore accelerating downward.

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Worked Example 3: Calculating Acceleration

A falling object has:

Mass = 60 kg

Weight = 588 N

Drag = 348 N

Calculate its acceleration.

First find the net force:

Fnet = Weight − Drag

Fnet = 588 − 348

Fnet = 240 N downward

Now use:

Fnet = ma

240 = 60a

a = 4.0 m/s²

Acceleration = 4.0 m/s² downward

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Worked Example 4: Parachute Opens

A skydiver has a weight of 700 N. Immediately after the parachute opens, the upward drag force is 1,900 N.

Calculate the resultant force.

Taking upward as positive:

Fnet = Drag − Weight

Fnet = 1900 − 700

Fnet = 1200 N upward

The skydiver is still moving downward, but the acceleration is upward.

Therefore, the skydiver slows down.

This demonstrates an important idea:

The direction of acceleration does not have to be the same as the direction of motion.

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Drag in Vehicles

Cars experience air resistance as they move through the atmosphere.

At higher speeds, aerodynamic drag becomes increasingly important.

Engineers reduce drag by designing cars with:

• streamlined shapes
• smooth body surfaces
• carefully designed front ends
• controlled airflow underneath the vehicle
• reduced unnecessary frontal area

Reducing drag can decrease the energy required to maintain high speeds.

This can improve fuel economy or increase the driving range of electric vehicles.

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Drag in Cycling

Cyclists also experience substantial air resistance.

Competitive cyclists reduce drag by:

• lowering their body position
• wearing tight clothing
• using aerodynamic helmets
• using streamlined bicycles
• riding behind other cyclists

Riding behind another cyclist is called drafting. The leading cyclist changes the airflow, allowing the following cyclist to experience reduced aerodynamic resistance.

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Drag in Water

Drag is also extremely important for swimmers, boats, submarines, and aquatic animals.

Swimmers reduce drag by keeping their bodies streamlined.

Fish have evolved body shapes that allow them to move efficiently through water.

Submarines are similarly designed to reduce resistance while moving through water.

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Falling Through Liquids

Terminal velocity does not occur only in air.

Small objects falling through liquids can also reach terminal velocity.

For example, a ball bearing falling through oil experiences:

• weight downward
• drag upward
• buoyancy upward

As the ball speeds up, drag increases.

Eventually the upward forces balance the downward weight.

The ball then falls at constant velocity.

Experiments like this can be used to investigate the viscosity of liquids.

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Drag and Energy

Drag transfers energy.

For example, when a car moves through air, some of the car's mechanical energy is transferred to the surrounding air and eventually becomes thermal energy and turbulent motion.

Similarly, a falling object loses gravitational potential energy.

Some of this energy becomes kinetic energy while the object accelerates, and some is transferred to the surroundings because of drag.

At terminal velocity, the object's kinetic energy remains constant because its speed is constant, while gravitational potential energy continues to decrease and energy continues to be transferred to the surroundings.

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Did You Know?

A skydiver can change terminal velocity without changing mass simply by changing body position.

Spreading the arms and legs increases the effective area and drag.

A more streamlined, head-down position reduces drag and allows a higher falling speed.

This means terminal velocity is not simply a property of an object's mass—it depends on how the object interacts with the surrounding fluid.

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Common Mistakes

Mistake 1: Saying drag is always constant

Drag generally changes with speed.

Mistake 2: Saying terminal velocity means the object stops

At terminal velocity, the object continues moving at constant velocity.

Mistake 3: Saying there are no forces at terminal velocity

Forces still act. They are simply balanced.

For a falling object:

Drag = Weight

Mistake 4: Saying acceleration is constant throughout the fall

As drag increases, the net force decreases, so acceleration also decreases.

Mistake 5: Assuming drag always points upward

Drag acts opposite to relative motion through the fluid. It points upward for an object falling through still air, but not in every situation.

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Analyzing Drag Problems

A useful strategy is:

1. Identify the direction of motion.
2. Draw a free-body diagram.
3. Identify weight, drag, and any other forces.
4. Determine the direction of the net force.
5. Use Fnet = ma if calculations are required.
6. Decide whether the object is speeding up, slowing down, or moving at constant velocity.
7. Check whether the forces are balanced.

Remember:

Weight > drag → downward acceleration

Weight = drag → zero acceleration

Drag > weight → upward acceleration

The object's actual direction of motion must also be considered when deciding whether it is speeding up or slowing down.

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Key Terms

Fluid: A substance that can flow, including liquids and gases.

Drag: A resistive force acting against relative motion through a fluid.

Air resistance: Drag produced by motion relative to air.

Terminal velocity: The constant velocity reached when the resultant force becomes zero.

Cross-sectional area: The area of an object presented to the fluid flow.

Streamlined: Shaped to reduce drag as fluid flows around an object.

Drag coefficient: A number describing how strongly an object's shape contributes to aerodynamic or fluid drag.

Fluid density: Mass per unit volume of a fluid.

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Key Equations

Newton's Second Law:

Fnet = ma

Weight:

Fg = mg

For a falling object:

Fnet = Fg − Fd

At terminal velocity:

Fd = Fg

Therefore:

Fnet = 0

and:

a = 0

A common model for drag:

Fd = ½ρCdAv²

Terminal velocity under this model:

vt = √(2mg / ρCdA)

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Key Takeaways

• Drag is a resistive force produced when an object moves relative to a fluid.
• Both liquids and gases are fluids.
• Air resistance is a type of drag.
• Drag acts opposite to relative motion through the fluid.
• Drag generally increases as speed increases.
• Drag is affected by speed, shape, cross-sectional area, and fluid density.
• A falling object initially accelerates because its weight is greater than drag.
• As its speed increases, drag increases and its acceleration decreases.
• Terminal velocity occurs when the forces become balanced.
• At terminal velocity, net force = 0 and acceleration = 0.
• An object at terminal velocity is still moving.
• Increasing cross-sectional area generally lowers terminal velocity.
• Increasing mass generally raises terminal velocity when other factors remain unchanged.
• Parachutes work by greatly increasing drag and producing a much lower terminal velocity.
• Drag forces are important in the design of vehicles, aircraft, sports equipment, boats, and many other technologies.