Business Velocity: a Newtonian Perspective

Earlier this week I came across a YouTube clip featuring a well known “business futurist” lecturing an HR audience on the concept of building business velocity. Shortly afterward, I came across a similar AT&T video on business velocity accompanied by the following summary quote from David Murray:

“Marketing video for AT&T. They handed me a bunch of boring interviews and the title “Business Velocity” and asked me to make something out of it…I still have no idea what these people are talking about!”

David, the good news is you’re not alone! Business velocity is one of those marketing buzzwords generally used to hawk a wide array of products and services, ranging from Business Process Management Software to Cloud Computing. From large corporations like AT&T, to self-proclaimed business futurists, everyone  talks about business velocity, but to my knowledge, no one has actually defined it in quantitative terms.

Those of you who read my last posting know how I feel about business terms that lack quantitative definition, so I thought this would be an ideal opportunity to explore the concept of business velocity through the lens of Newtonian mechanics.

Isaac Newton’s three laws of motion established the basis for classical mechanics. They describe the relationship between the forces acting on a body and its resulting motion. Loosely translated, Newton’s first law states that an object in motion will stay in motion unless acted upon by an external force. The concept is best illustrated by Newton’s cradle, which most of us have seen at one time or another.

Largely a restatement of the law of inertia originally formulated by Galileo, Newton’s first law proclaims that an object cannot change its velocity spontaneously. If something is moving along at a constant speed, it will continue to move along at the same constant speed unless acted on by an external force. It cannot, on its own, speed up, slow down, or change direction.

Velocity is a vector quantity. It provides an indication of how fast something is moving in a given direction. In mechanics, velocity is defined as the ratio of the change in distance (d) per change in unit time (t).

v =  ∆d / ∆ t

Defining Business Velocity

Being generally concerned with the motion of bodies, Newtonian mechanics uses a change in position (distance) as the basis for defining velocity. When we shift our context from mechanics to business, we’re forced to propose a new basis.

Businesses exist to make a profit. Profit is defined as revenue minus expense.  If we equate the concept of top-line business revenue (r) to distance (d) in mechanics, we can propose a reasonably valid way to define business velocity in quantitative terms. What we’re suggesting is to define business velocity (Vb) as the ratio of change in top-line revenue (r) per change in unit time (t).

Vb = ∆r / ∆t


Vb (avg) = r2 – r1 / t2 – t1

Notice that our proposed definition also provides us with a system of units.  If our unit of revenue is 1 dollar, and our unit of time is 1 hour, the unit of business velocity is 1 dollar per hour (1 dph). Stated simply, a revenue increase of $60 in a period of 1 hour equals a business velocity of $60 per hour.

While seemingly arbitrary, our choice of units (dph) is no less valid than miles per hour (mph) or feet per second (fps) in the realm of mechanics.

From a purely mathematical viewpoint, there’s no restriction on the value that can be assigned to t in the equation. We can use seconds, minutes, hours, days, quarters, etc. Practically speaking, business reporting is done on a quarterly basis.  Since the average calendar quarter is 91 days, we can divide quarterly changes in revenue by 2,148 (91 days per quarter • 24 hours per day) to yield a unit system of dollars per hour.

Examples of Business Velocity

To help illustrate our definition of business velocity, let’s examine top line revenue growth for three of the largest U.S. wireless carriers: AT&T, Verizon and Sprint.  The following graph contains revenue (rounded to billions of dollars) as detailed in each company’s annual report.

Notice that Sprint’s revenue is constant at $8.3B per quarter. Based on our definition, Sprint’s average business velocity across any quarter can be calculated as follows:

vSprint  = ($8.3B – $8.3B) / 2,184 hours  = 0 dph.

The result: Sprint exhibits no business velocity across any period measured. This appears to be entirely consistent with Newton’s first law of motion: an object moving along with a given velocity will continue to move along at the same velocity, unless acted on by an external force.

What about AT&T? For the period 30-Dec-2010 to 31-Mar-2011, AT&T’s reported revenue is also constant at $31.4B.  Therefore, AT&T’s business velocity during the period is zero.

vAT&T  = ($31.4B – $31.4B) / 2,184 hours  = 0 dph.

Verizon, on the other hand, demonstrates revenue growth across all four quarters. We can calculate Verizon’s business velocity across the entire period as:

vVerizon  = ($27.9B – $26.3B) / (2,184 * 4) ≈ $183,000 dph.

In addition, notice that from 30-Dec-2010 to 30-Jun-2011, the graph of Verizon’s revenue is linear, indicating constant acceleration.  In mechanics, acceleration (a) is defined as the time rate of change of velocity. The same definition should also hold true in the business context. Therefore, we can propose a quantitative definition of business acceleration as follows:

ab = ∆v / ∆t

In situations where acceleration appears to be constant, the equations of motion can be derived algebraically, without resorting to calculus, as follows:

  v2  = v1 + at   or  (v2 – v1) / (t2 – t1)  = a

Using the equation, we can calculate Verizon’s business acceleration as a function of velocity within our proposed system of units.

($27.5B – $26.3B) / ( 2 • 2,184)  =  a ≈ $274,725 dph2

The natural question that emerges at this point is: Why was Verizon able to generate business velocity while Sprint and AT&T were not? Unfortunately, we’re not yet ready to answer that question.  What we can say, with certainty,  is that according to Newton’s first law of motion, an external force must have been involved.
In terms of our exploration, we are not yet in a position to be able to analyze the concept of force in terms of the classic equation  F = ma.  We still lack a business definition for the concept of mass. However, by developing  a quantitative definition of business velocity – one which enables us to measure acceleration -  we’ve clearly set the stage.
Issac Newton embodied the interrelationship between the physical concepts of force, mass, and acceleration into his three laws of motion. These universal principles, so elegant in their simplicity, help explain and predict the motion of objects in the natural world. Applying Newton’s concepts will enable us to explore the causal relationship between force, mass, and acceleration in a business context in more meaningful way.
p.s. – this post is dedicated to David Murray.

5 thoughts on “Business Velocity: a Newtonian Perspective

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