Solving the 1st Half of the Problem to Get to the 2nd

A problem well stated is a problem half-solved.
Charles F. Kettering

A few months ago, I wrote about the ill-fated AGM-183A hypersonic missile. While its engineering parameters were well-known, its budget limitations were not. Funded to about $1.7B for its development, Lockheed Martin said its first unit cost would be about $42M. At the same time, the Congressional Budget Office thought the USG would be able to afford 100 of them at their eventual per-unit price of $15M to $18M. As a variation of the chart below revealed (C), the chance of that happening was significantly less than one in one million quadrillion, as that price put it at 108 Standard Deviations past the market’s Upper Demand Frontier. Eventually, budget realism entered the picture, and the United States Air Force stopped funding the program. In the process, it validated their Demand Frontier.

For all the work we spend extending the boundaries of engineering, we must understand that trying to exceed a well-defined Demand Frontier by leaps and bounds never works.

To know what we can do, we must first know what we can’t. That’s part of the 1st half of the problem. The AGM-183A didn’t get past that.

LM did quite a bit better with its stealthy AGM-158B, also known as the JASSM-ER, in (A) below. At the time of the study, it was the most expensive air-to-surface missile in the industry. In the 20 years shown in (C) (1997-2016), LM sold 275 units at an inflation-adjusted 2024 price of $2.5M, with the AGM-158B helping to form the market’s Upper Demand Frontier. Note that that curve is relatively flat, with a slope of -0.533. That meant the USG spent more money on the market’s lower-priced part than its upper bit.

A recent headline noted that Russia knocked down over 150 Ukrainian drones. The ineffectiveness indicates the need for missiles to be invisible to the enemy. Getting smaller and stealthier will help.

Enter the prospect of much smaller, less expensive, and (presumably stealthy) cruise missiles, the air-to-surface (specifically, anti-ship) ordnance proposed by American defense startup Ares Industries shown in (B). Designed to attack smaller vessels, the company has set a target price of $300K per missile. Of course, whether or not they pull this off remains to be seen, but the attempt is admirable, as the low price enables the purchase of up to tens of thousands of units over two decades (C). It would add flexibility in the inventory, letting operators swap expensive devices for cheaper ones when smaller packages can do the job.

In (C), since Glide Bombs cost a fraction (about 1/8 for the same payload*velocity and range) of missiles, planners can afford to buy more of these devices than powered missiles. One could imagine a future in which stealthy glide bombs dropped from unmanned drones would lower operational costs and pilot risk while increasing mission success rates.

 

Uphill to Stupid: Universality Abounds

All schools and colleges have two great functions: to confer and conceal valuable knowledge.
Mark Twain

Some writers have gained more attention than their ideas merit. It takes little thought to discard them.

Take Karl Marx and his school of thought, for example. In his Communist Manifesto, he wrote, ” Modern bourgeois society… is like the sorcerer who is no longer able to control the powers of the nether world.” Later, in his Capital: A Critique of Political Economy, Marx stated, “So far, no chemist has ever discovered exchange-value in …a diamond.” He wants you to believe that the bourgeois economy runs by magic.

Hypernomics knows better. And so do you. A diamond’s value is a function of its carats, color, clarity, and cut. Marx certainly knew of the Hope Diamond and that it was worth more than smaller stones. He was pulling the wool over readers’ eyes. There is not a lick of sorcery in diamond valuations. Thus, his view about diamonds is downhill of stupidity. He was more sinister than that. Instead, he concealed valuable knowledge. This would-be sleight of hand had implications for states that followed his lead.

In 1985, the USSR artificially constrained all salaries to 400 rubles or less per month (Alexeev, Michael V., et al., “Income Distribution in the USSR in the 1980s,” 27 Nov 1992), defying conventional (i.e., non-Marxist) economic wisdom. Doctors made little more than janitors. It made sense to the central planners. And then their economy collapsed—not despite their best efforts, but because of them.

When it comes to Valuing physical products (like a flawless, colorless, round, brilliant two-carat diamond or an Oscar II nuclear cruise missile submarine weighing nearly 15K tons with a top speed of 32 knots) instead of people, there’s no option other than Hypernomics.

In (C) below, the angled plane projects the value of Russian nuclear submarines using performance and price data from 20 and 57 ship classes in the United States and Russia, respectively. The equation used for that surface has a p-value of 9.85E-40. In (B), reflecting the same equation with its step function, the US pays about 60% more for the same tonnage and speed as comparable Russian boats, likely due to factors not considered separately in this equation (such as safety, max depth, comfort, etc.). All navies have behaved like that since they began.

With (A), the US and Russian navies abide by statistically significant but distinctly different Demand Frontiers, each with a p-value of about 0.03. Demand comes not from Marxist rants but from how all buyers purchase goods as their prices change. The slopes may change, but the central tenet does not.

When next you meet a Marxist, tell them the Eastern Bloc buys naval vessels the same way as the West. In other words, they buy like the bourgeoisie. And that is so bourgeois.

Which, despite the would-be disparaging tone, is a good thing.

Market Limits and Infinite Dimensional Compression

Genius may have its limitations, but stupidity is not thus handicapped.
Elbert Green Hubbard

The International Cost Estimating and Analysis Association (ICEAA) recently held its annual Professional Development & Training Workshop in Minneapolis, Minnesota. This event, a cornerstone of professional development for our members, was a remarkable success. I submitted a paper to it, and it won the award for best paper overall.

Market Dimensional Expansion, Collapse, Costs, and Viability” delved into several crucial yet under-explored areas. Dimensional expansion and collapse are vital to comprehending market evolution. In it, I unveiled a groundbreaking method to compress standard 3D Cartesian Coordinate Systems into as many as 16 dimensions. Theoretically, there is no upper limit to the number of dimensions that can be depicted using these methods. Equally significant was the exploration of multiple views on Demand Frontiers.

In (D), I plotted the ten-year demand figures for 95 Western Bloc business aircraft, with the horizontal axis for their quantities and the prices on the vertical. Several crucial limitations become evident when one does that.

An Outer Demand Frontier reflects the market’s saturation threshold. Any model attempting to exceed this line will find that the market has exhausted its buyers. One can drop one’s price and gain more sales, but this line is very steep and will soon intersect any Learning Curve associated with the aircraft model that forms it. Note that none of the planes in the study vastly exceeded this limit.

The Lower Demand Frontier reveals a market’s margin limitation. There are planes priced below this line but fall into the General Aviation category. They are not for business travel due to the stricter regulations by which Business Aircraft abide.

Inner Demand Frontiers are efficiency-limited. Planes to the left of this line are either 1) reconfigured airliners (where the main airliner line keeps the learning going), 2) ramping up production, 3) winding down their line, or 4) underwritten by governments. In this case, all Textron planes are going extinct, as the company gave up building these aircraft types. The Dassault planes benefited from a large subsidy from the French government, and Piaggio got the same treatment from the Italian state.

The Upper Demand Frontier is the limit that took down the Aerion AS2, as it attempted to go far beyond it. In a different market, this made the B-2 bomber stop at 21 units rather than the 132 vehicles the USAF sought.

In sum, it pays to know where your contest’s boundaries lie. In markets, as in competitive games, there are boundaries. In business, your buyers form those boundaries. Knowing what your buyers can and can’t afford is critical to developing a product with a chance for success.


In (A), I hold a 2D Demand Plane in one hand, and a 3D Value Space in the other. The paper I gave using this concept won the awards in (B), allowing me to speak to 450 People (C). Among other things, my paper addressed markets’ Demand Frontiers (D).

Safety Pays

We think we know what we’re doing / We don’t know a thing / It’s all in the past now / Money changes everything.
Cyndi Lauper

When trying to increase profits, many companies often chant the same old mantra, “Let’s cut costs.”

Aerospace is not immune to such cries. Recent events at The Boeing Company have highlighted how hurrying planes out the door led to a door bolting off a plane. The no-door idea works for Jeep but is a bad look on an airliner. Many see safety requirements as just another hurdle to jump on the way to making money. It’s a cost once sunk, never to be seen again.

But data analysis tells a different story.

All the excellent work Boeing (before Max) and others did to reduce loss rates increased airliner Value (sustainable prices). Below, the Boeing 737-800 had a hull loss rate of 0.2 per million flights. At less than 1/31st of the Tupolev Tu-204 loss rate, it explains how the Boeing 737 series commanded a higher price and sold over 100 times as many as its Russian counterpart with less capacity, range, and speed.

Diligent workers want to put out the best possible products. Keeping their established quality helps the brand’s Value and bottom line.

Take 52 turboprop and jet airliners (19 shown here) and determine their Value (sustainable price) based on their Payload and Maximum speed in MPH. You’ll get a nicely correlated answer. But add their loss rates into the mix, and you’ll get a better one (its p-value 1.47E-05). Being 10X safer costs time and money but adds over 50% to airliner Value.

A New Twins Thought Experiment

The formulation of a problem is often more essential than its solution
Albert Einstein

Einstein performed a thought experiment in which he imagined one of a pair of twins traveling near the speed of light while the other remained fixed on Earth. The faster twin, he stated, would age less quickly due to time dilation. Experimentation proved his theory with a pair of synchronized clocks, one flying in a jet, the other on the ground, as the jet clock recorded less time. This theory is the basis of GPS.

That method applies to my discovery of Hypernomics. I imagine one twin (A) plotting the 1) horsepower, 2) range, and 3) prices of electric cars. Meanwhile, in (B), her sister plots the 4) quantities sold and 3) prices of those models. In (C), I observed that as (A) and (B) have the same vertical axis, they combine to form a 4D system, where statistically significant relationships form on both sides, linking the opposing forces of Value and Demand. These forces have worked for all markets since the beginning of markets.

Einstein didn’t open a relativity shop for his theory. But you can apply these 4D methods and many more to your business problems, as my revolutionary book, Hypernomics (D), describes.

Hyperplane Economics: Beyond Conventional Boundaries

Holy Hyperplanes Batman!
Dick (aka Robin): Gosh, Economics is sure a dull subject.
Bruce (aka Batman): Oh, you must be jesting, Dick. Economics dull? The glamour, the romance of commerce. Hmm. It’s the very lifeblood of our country’s society.

The Batman TV Series, The Joker’s Last Laugh [2.47]

You’d be bored with economics, too, if you didn’t get a chance to whip out a hyperplane or two. It turns out that they are not just some superfluous hidden geometries but ways to see and solve unseen problems.

Here’s a riddle: How do you model the options for a new bomber?

Here’s how Hypernomics approaches that. First, work out the Demand Frontier for planes of that ilk, as shown in (A) below. Then, find a quantity or two you like and their related maximum prices. In the adjacent Value Space, derive the Value of the bombers as a function of speed, range, and quantity. Set the quantity in the Value Space to your limits along the Demand Frontier. Then, plot the hyperplanes for Value and let them intersect your horizontal price-limited planes. As straight lines in log space, those intersections appear as the curves in the linear plane (B), revealing your options.

For more insight, consider adding payload and stealthiness to the mix.

Same Function, Different Form, Common Links

The moment of truth, the sudden emergence of new insight, is an act of intuition. Such intuitions give the appearance of miraculous flashes, or short circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links.
Arthur Koestler

Invisible links. Poppycock. We don’t need no stinking invisible links.

For too long, many have thought market actions were largely mysterious, their forces hidden, and actions unpredictable. When it comes to product demand, that is complete nonsense. Even when collections of products look different but do the same thing, they behave in ways we can predict.

A Invisible links. Poppycock. We don’t need no stinking invisible links.

For too long, many have thought market actions were largely mysterious, their forces hidden, and actions unpredictable. When it comes to product demand, that is complete nonsense. Even when collections of products look different but do the same thing, they behave in ways we can predict.

A Raven UAV doesn’t look anything like a Topaz satellite. Yet, doing the same mission using different altitudes, payloads, and speeds, they are bound by the same Demand Frontier, one that limits the arena’s most highly rewarded performers. If you prove worthy enough to be on the field of play, you often find a certain lower guarantee of recompense, known as Minimum Demand.

Such boundaries are only mysterious if you don’t do Hypernomics. doesn’t look anything like a Topaz satellite. Yet, doing the same mission using different altitudes, payloads, and speeds, they are bound by the same Demand Frontier, one that limits the arena’s most highly rewarded performers. If you prove worthy enough to be on the field of play, you often find a certain lower guarantee of recompense, known as Minimum Demand.

Such boundaries are only mysterious if you don’t do Hypernomics.

Spy satellites, military satellites, and Unmanned Aerial Vehicles (UAVs or drones) all perform the same mission and face identical financial limits. Below is an Upper Demand Frontier that includes models of all three groups. With a slope of -1.38, is steep (inelastic).That means more money is spent on five Topaz Spy Sats (5*$9.4B = $47B) than the 19,000 Raven Drones (19,000 *$25K= $475M).The steeper (-1.96) Minimum Demand Frontier reveals that one Mercury Spy Sat ($2B) fetches more than 19,000 RQ-I4s (I9K*$3K = $57M).

Same Function, Different Form, Same Equation

California sunlight / Sweet Calcutta rain / Honolulu starbright / The song remains the same.
Led Zeppelin

Modern surveillance demands a lot of different platforms. The Russians run ELectronic INTelligence (ELINT) satellites over Hawaii, California, and the rest of the US (A). Western forces must get the same insight to be as well-informed.

We can get this data from airborne platforms outside of manned systems (such as the U-2 Dragon Lady, the E-3 Sentry, and the E-2C Hawkeye) by using satellites and Unmanned Air Vehicles (UAVs).

It turns out we can predict the Value (sustainable price) of Western Bloc satellites and UAVs using the same equation. In (B), with 30 Sats on the left and 30 UAVs on the right, we predict the Value of the US Mercury ELINT satellite using an equation considering 1) Payload, 2) Max MPH, 3) Altitude, and 4) Quantity sold. The Israeli Orbiter UAV (C) estimate using the same equation is highlighted in (D). With an adjusted R2 of 96.1%, its p-value is 8.83E-39.

As you might imagine, the Inner and Upper Demand Frontiers for these devices are highly correlated, too, giving direction on purchases.

More on that in another post.

Strategy Rethought

You can’t always get what you want/But if you try sometimes, well, you just might find/You get what you need
The Rolling Stones

There’s a trend in defense matters to want the absolute best always. We tried to get 132 bombers with long range, massive payloads, and very low radar signatures. We got 21 B-2s. The USAF wanted 750 frontline stealth fighters. It received 187 F-22s. Nobody, it seemed, ever paid close attention to the budgets allocated to missile-carrying aircraft.

We see the same thing now in the US hypersonic missile market. The Congressional Budget Office (CBO) thinks it can buy 100 of the Lockheed Martin AGM-183 ARRWs (or a like device) for an average price of $14M (2016$), with a range of 1000 miles. For an agency with “Budget” in its title, you might think they would have done the analysis below. If they had, they’d find their projection is 108 standard deviations past that market’s highly correlated Demand Frontier.

We’ve paid heavily to make our frontline bombers invisible to radar – don’t imagine they need to use missiles with stand-off ranges to accomplish hypersonic missions.

The solution is clear: make any hypersonic missile smaller and cheaper with less range and payload and fly it closer to the target.

China claims to fly them. Russia wants them, too. It makes sense that the USA must also have these hypersonic weapons.

But, as in all budget matters, there are limits. At the current CBO projection for the average cost of the 100th missile of that ilk ($14M in 2016$)1,2 that price point is 108 std devs past the budget limit. The solution is to make a much smaller missile with far less range and fly it closer to its targets.

Nailing the X-Ray and Gutting “The Law of Supply and Demand”

You can observe a lot by watching.
Yogi Berra

Dante Autullo went to a hospital complaining of nausea and a headache. A passing diagnosis might have been that he had the flu. But when his doctors asked him about what he had been doing, X-rays showed that as he was using a nail gun, a nail he thought whizzed past his head went into it instead (A). They operated; he’s okay.

Easy answers have a lure. After all, who wants to dive deeply into a flu case? But details matter. Easy answers aren’t always right. Just ask Dante.

The draw to misguided and overly simplistic phenomena applies to “The Law of Supply and Demand.” As we see in (B), given their postulates (i.e., flawed assumptions), they propose a single market equilibrium point. Every time they show such an example, it never has real-world data. It is always all made up.

I’m not going to stand for it. Neither should you.

Readers of this column know actual market behavior, based on verifiable data, looks more like (C), where buyers pay for aircraft cabin volume and speed (in the left-hand Value Space) as limited by their available funds (on the right-hand Demand Plane). Upcoming posts will give you more reasons to listen to reason.