"1. The Rim will provide the real Lateral and Radial Stiffness (ie a flexy rim will always be flexy regardless of spoke tension)"
I'd suggest... one can significantly increase the stiffness of a flexy rim with spokes that do not flex/stretch easily. IMO the 'real' stiffness is again a function of the entire unit.
"He was testing an actual wheel. That's "real world". (Rinard.. please excuse typo earlier)
Very true.. I included referencing the online book per wheel building.
My point.. is simply this: discussing present day real world examples I can learn something tangible from. List the components.. the conditions the outcomes were derived from.. then how that outcome is related to that SET of components. IE: what works.... and what does not... and WHY.
This in-depth discussion.. and how to cheat the scale building strong wheels... I find very informative.
Anyone ever build a triplet with the NDS tension higher than the DS?

Anyone ever build a triplet with the NDS tension higher than the DS?

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people.duke.edu ... The behavior of bicycle wheels subjected to static radial loads can be accurately modeled by idealizing the system of interlacing spokes as a linear elastic foundation of uniform stiffness per length of circumference. [b]The spoke pattern affects the over-all radial stiffness of the wheel more than it affects the spoke strains.[/b]

From a numerical analysis, the spoking pattern has the greatest impact on the spoke strains when the wheel is subjected to large lateral loads, such as during cornering. In this case, wheels with longer spokes have lower strains than do wheels with shorter spokes.

... it may only be concluded that static spoke strain due to radial loads are roughly independent of the spoke pattern, for the wheels in this study. Static spoke strains are, however, influenced by the spoke pattern when lateral loads are applied to the rim. In this case, wheels with the shortest spokes have the highest spoke strains.

The fatigue resistance of the spokes, the spoke diameter, the arrangement of the spokes, and the stiffness of the rim influence wheel stiffness and fatigue life. Wheels with 2X, 3X, and 4X spoke patterns all have similar spoke strains when subjected to radial loads. The fatigue resistance of spoked wheels to steady cycling loads is very high for most typical service conditions.

www.rouesartisanales.com ... Frontal stiffness
Coming back to our frontal stiffness test, the wheel is fixed by its axle, then crushed. The force applied is determined by software which records deformation at the same time. The wheels deform very little because of several parameters playing an important role in the vertical deformation. The rim height and its high frontal stiffness are not really prone to deform easily. Shallower rims obviously deform more easily than deep rims because they are not as stiff. The spokes also play a role: their number, crossing pattern, tension and spoke stiffness (material, cross section) all have an influence on overall vertical stiffness of the wheel. A low cross section spoke with low spoke tension will deform or lose its stiffness quicker than a high cross section and high tensioned spoke. The hub plays a role too, but its influence will be smaller than the two first.

Rear wheels are not as stiff as front wheels because of the bracing angle difference on the two sides of the rear wheel. A rear wheel with a shallow rim, with low tensioned spokes, will vertically be easier to deform than a deep rim wheel with high tensioned spokes. A special case worth highlighting is an exception which concerns the Shimano 7850 C24TU and C50TU wheels, but also the Mavic Cosmic Carbone Ultimate offering higher frontal stiffness front than rear. The high spokes tension seem to be responsible of this phenomenon.

Lateral stiffness
Beside this, when the rider pushes the pedals, the torque transmitted through the spokes deforms the wheel because of the bracing angles creating a lateral component: even when sitting in the saddle, the rear wheels moves between the brake pads when a rider stomps on the pedals. So the rear wheel must be as stiff as possible in order not to slip away when transferring the power. The lateral stiffness of a conventional wheel depends on several parameters. First of all, the rim will determine the stiffness of the wheel by its depth, its torsional stiffness and spoke length. Then, the spokes give the wheel integrity and play a role in the stiffness according to their tension and their cross section. Finally, according to Mavic, the most important parameter is the bracing angle, which is the distance between the flanges of the hubs.
Thus, in order to increase the lateral stiffness of a wheel one needs to:
- use a stiff and deep rim which will also comes with shorter spokes
- use larger spokes
- increase the bracing angle: hubs with flanges as far as possible
- high tensioned spokes to delay the moment when the wheel loses all its stiffness

However, all these improvements come with a weight penalty so we have to make compromises and identify the improvements with a big impact on stiffness but the smallest weight penalty: deep rim (increasing aero properties too), hubs with widely spaced flanges. Flange diameter will play a role too but it will come with an important weight penalty.

A high deflection of the rim between the brake pads may slow the rider during the acceleration phase if the rim hits the pad. The parameters playing a role here are not well known but when digging deep inside the stiffness/deflections at 180° sheet, there are at least two important parameters:
- the rim depth: the shallower it is, the smaller are the deflections between the brake pads, but the lower is the lateral stiffness of the wheel
- the spoking: the higher is the spoke count, the lower are the deflections between the brake pads, and the higher is the wheel stiffness.

There are some special cases, especially from the biggest manufacturers, where the rear wheels are as stiff or stiffer than the front wheels. This comes from the optimisation of the wheel components: special spokings, extreme tensions, unusual constructions (Mavic R-SYS for example). A heavy rider stresses more the wheels than a light rider. If this heavy rider uses a too flexy wheel, it will easily go out of shape while sprinting and its spokes (most of the time the rear wheel non drive side spokes) will often lose their tension. This has three consequences: the wheel will go out of true if the spokes are not locked, the rider will feel the lack of stiffness which is poor for the performance and the spokes will have a shorter working life (and break).

Conclusion
The feeling of efficiency and performance on the road mainly comes from the inertia of the wheels but lateral stiffness is important too. It also is not necessary to get the stiffest wheel at all costs because this may compromise other characteristics of the wheel. High lateral stiffness often means a heavier wheel, meaning higher inertia and therefore harder accelerations or more difficult climbs. Ideally, one should choose the wheels with the best weight to stiffness ratio, considering your own weight and it’s important not to forget aerodynamics.
Recommendations to optimise racing performance ... Basically, only heavy riders, or racers looking for extreme performance need stiffness at all cost.
- Over 80kg, the racer should focus on wheels over 40N/mm of lateral stiffness.
- 70-80kg, wheels under 35N/mm are likely to impair performance in some race situations.
- 60 and 70kg would be best avoiding wheels with lateral stiffness below 30N/mm.

Tortrional stiffness is no more dependent of spoke tension than lateral stiffness is so I cannot see how having NDS tension 120% of DS is ever going to help.

Frontal stiffness
Coming back to our frontal stiffness test, the wheel is fixed by its axle, then crushed. The force applied is determined by software which records deformation at the same time. The wheels deform very little because of several parameters playing an important role in the vertical deformation. The rim height and its high frontal stiffness are not really prone to deform easily. Shallower rims obviously deform more easily than deep rims because they are not as stiff. The spokes also play a role: their number, crossing pattern, tension and spoke stiffness (material, cross section) all have an influence on overall vertical stiffness of the wheel. A low cross section spoke with low spoke tension will deform or lose its stiffness quicker than a high cross section and high tensioned spoke. The hub plays a role too, but its influence will be smaller than the two first.

Lateral stiffness
Beside this, when the rider pushes the pedals, the torque transmitted through the spokes deforms the wheel because of the bracing angles creating a lateral component: even when sitting in the saddle, the rear wheels moves between the brake pads when a rider stomps on the pedals. So the rear wheel must be as stiff as possible in order not to slip away when transferring the power. The lateral stiffness of a conventional wheel depends on several parameters. First of all, the rim will determine the stiffness of the wheel by its depth, its torsional stiffness and spoke length. Then, the spokes give the wheel integrity and play a role in the stiffness according to their tension and their cross section. Finally, according to Mavic, the most important parameter is the bracing angle, which is the distance between the flanges of the hubs.
Thus, in order to increase the lateral stiffness of a wheel one needs to:
- use a stiff and deep rim which will also comes with shorter spokes
- use larger spokes
- increase the bracing angle: hubs with flanges as far as possible
- high tensioned spokes to delay the moment when the wheel loses all its stiffness