More and more power generation from renewable energy sources is now- a- days being desired with the objective of meeting out the carbon footprint standards. The fossil fuel based power plants being major emitters of Co2 in the environment engender green house heating. Solar energy has proven itself to be the most viable solution for renewable energy based power production. PV cells arranged in the form of solar panels are now- a- days common sight on the roof- tops of buildings for meting out their energy requirements. The panels are normally fixed at an appropriate angle of inclination depending on the latitude and longitude of the site. Now- a- days trackers are also used with the panels to orient them in the line with the movement of sun such that it continuously faces maximum amount of insolation for maximizing the energy yield. The tracking however being passive in nature requires energy input for operation which becomes a liability from the point of the total energy output.

There have been attempts to optimize the solar panel design for obtaining maximum output power from them in the past. The solar tree designs are an effort in the same direction. Solar tree is an innovative concept of arranging the PV panels in the form of radially protruding outward branches from a central trunk replicating tree like appearance. There is spiral arrangement of braches on the trunk from bottom to top having “ n” spiral turns around it and a total of “ p” number of braches coming out from bottom to top along the spiral path. Normally a phyllotaxic arrangement of branches and leaves based on Fibonacci ratios such as 1/ 3, 2/ 5, 3/ 8 and 5/ 13 are taken as reference for deciding the ratio n: p in a solar tree. This arrangement helps in optimized capturing of falling insolation and its conversion into electrical energy in a given time duration as compared to a fixed panel. A solar tree based on 2/ 5 Fibonacci ratio depicting the branch arrangement in a oak tree is designed and its energy output in a particular time duration is compared with a fixed solar panel of equal capacity facing same amount of solar insolation. The pressure of growing population has resulted in shrinking of agricultural lands in many countries due to construction and industrialization. Moreover, the crisis and growing demand of food each year has resulted in pressure to create more and more cultivable land resources. The conventional PV plants have panels generally erected on land rendering it un- useful for agriculture. The solar trees have to some extent have provided solution to this situation as they require just 1% of the land in comparison with the conventional PV plants[ 6, 7].

More and more power generation from renewable energy sources is now- a- days being desired with the objective of meeting out the carbon footprint standards. The fossil fuel based power plants being major emitters of Co2 in the environment engender green house heating. Solar energy has

proven itself to be the most viable solution for renewable energy based power production. PV cells arranged in the form of solar panels are now- a- days common sight on the roof- tops of buildings for meting out their energy requirements. The panels are normally fixed at an appropriate angle of inclination depending on the latitude and longitude of the site. Now- a- days trackers are also used with the panels to orient them in the line with the movement of sun such that it continuously faces maximum amount of insolation for maximizing the energy yield. The tracking however being passive in nature requires energy input for operation which becomes a liability from the point of the total energy output.

There have been attempts to optimize the solar panel designs for obtaining maximum output power from them in the past. The solar tree designs are an effort in the same direction. Solar tree is an innovative concept of arranging the PV panels in the form of radially protruding outward branches from a central trunk replicating tree like appearance. There is spiral arrangement of braches on the trunk from bottom to top having “ n” spiral turns around it and a total of “ p” number of braches coming out from bottom to top alongthe spiral path. Normally a phyllotaxic arrangement of branches and leaves based on Fibonacci ratios such as 1/ 3, 2/ 5, 3/ 8 and 5/ 13 are

taken as reference for deciding the ratio n: p in a solar tree. This arrangement helps in optimized capturing of falling insolation and itsconversion into electrical energy in a given time duration as compared to a fixed panel.

Nice question — phyllotaxy (the golden-angle spiral arrangement you see in sunflowers) is actually a very natural fit for a solar-tree: it spreads panels to reduce self-shading, gives near-uniform access to sky over all sun angles, and looks great. Below I give a practical, engineering-ready checklist plus design rules, key equations, a worked example for sizing a PV array to power a pump, and testing/simulation steps you can use to optimize a real installation.

Quick summary (takeaway)

Use phyllotactic spiral spacing (golden angle ≈ 137.5°) around a trunk to spread panels and minimize shading.

Tune radial spacing and vertical pitch so panels clear each other for the sun’s lowest winter altitude at your latitude.

Combine fixed optimized tilt (latitude or seasonally adjusted) or lightweight single-axis tracking per panel for big gains.

Use per-panel MPPT / microinverters, DC pumps, and smart controllers so harvested energy is used efficiently for irrigation.

Model first (ray tracing / PVsyst / simple geometry) and prototype before full build.

Design rules & geometry (phyllotaxy specifics)

Use the golden angle 137.507764° (commonly quoted as 137.5°) as the angular step between successive arms/branches. This yields a near-uniform radial distribution and minimizes overlap.

Radial spacing (r_n) — panels at index n placed at radius proportional to √n (typical phyllotaxis law). In practice, pick discrete radial rings and ensure:

Horizontal clearance between panel planes avoids shading at the minimum sun altitude (winter solstice).

Vertical pitch Δz between successive panels sized so that the projection of an upper panel does not fall on the lower one for the worst-case solar elevation.

Panel rotation about branch axis: orient module normal to the local incident sun direction on average (or keep them flat with tilt toward equator). A small rotation can reduce cosine losses across the day.

Tilt vs latitude: choose fixed tilt ≈ latitude for year-round performance or latitude ± seasonal adjustment. If you can add lightweight tracking (single-axis around vertical or horizontal axis per branch), you gain 10–25% annual energy capture.

Avoid dense clustering near trunk — keep first ring radius so cables/maintenance access and cooling are possible.

Electrical & system design to maximize usable energy

Per-panel MPPT or microinverters: critical because each panel on a tree sees different irradiance and orientation; centralized MPPT loses energy when strings mismatch.

Bifacial panels (if you can): take advantage of reflected irradiance from ground or integrated reflectors below branches.

DC pumps & motor-controllers: prefer brushless DC pumps with good efficiency and wide MPPT input range; direct-coupling to PV via MPPT (or battery buffer) reduces conversion losses.

Energy storage / buffer: small battery or supercapacitor to smooth short term intermittency; if irrigation can be scheduled during sun hours, storage can be minimized.

Power electronics: include soft start for pumps, surge protection, low-loss wiring (proper gauge for distance), and ground fault protection.

Hydraulics → sizing PV for irrigation (key formula + worked example)

Hydraulic energy required per day (Wh):

Mass m = ρ·V (ρ ≈ 1000 kg/m³)

Potential energy (J) = m·g·H (g = 9.81 m/s², H = head in m)

Convert J → Wh: divide by 3600.

Electrical energy required = (hydraulic Wh) / (pump efficiency).

PV energy required = (electrical Wh) / (system efficiency, incl. inverter, wiring, MPPT).

PV array power (W) ≈ PV energy required (Wh/day) / peak sun hours (h/day).

Worked example (common case): supply 5 m³/day to 20 m head.

V = 5 m³ → mass = 5,000 kg.

Hydraulic energy = 5,000 × 9.81 × 20 = 981,000 J.

Convert to Wh: 981,000 / 3,600 = 272.5 Wh (hydraulic energy).

Pump efficiency 60% → electrical = 272.5 / 0.60 = 454.17 Wh.

System losses (inverter, wiring, MPPT) assume 80% → PV must deliver 454.17 / 0.8 = 567.7 Wh/day.

If site has 5 peak sun hours/day → PV array size = 567.7 / 5 = 113.5 W.

Add safety margin ×1.3 → final recommended PV ≈ 150 W.

(You can plug your V, H, efficiencies and peak sun hours into the same steps.)

Optical / shading modeling & tools

Simulation is essential: do a 3D ray-trace or shading simulation across the year (hourly) to compute real energy yield, not just geometric clearance.

Tools: PVsyst (widely used), SketchUp + Ladybug/Dragonfly / Radiance, or custom Python raytracer.

Simulate worst-case winter sun path for shading and daily/yearly yield to decide radial/vertical spacing.

Prototype a single branch and measure irradiance over a week to calibrate model.

Structural, thermal, and maintenance considerations

Wind & loading: irregular geometry needs structural analysis (wind uplift, torsion). Use conservative safety factors for branch cantilevers.

Cooling & airflow: trees let air circulate — maintain minimum standoff from module to reduce temperature and increase efficiency.

Soiling & cleaning: plan access and angle to reduce soiling; consider hydrophobic coatings or tilt that sheds dust.

Lightning & grounding: tall structures require lightning protection and proper earthing for safety.

Control strategy (smart irrigation = maximize system usefulness)

Match irrigation schedule to peak PV generation where possible (midday watering) to minimize storage.

Weather forecasting + soil moisture sensors: use forecast-adjusted irrigation to conserve energy and water (delay irrigation on rainy days).

Pump control with variable speed drives and MPPT ensures pump power tracks available PV power and avoids unnecessary battery cycling.

Data logging & remote monitoring: log PV power, pump draw, soil moisture, and reservoir level to optimize long term.

Performance boosters (nice-to-have)

Bifacial modules + ground reflectors (albedo boosting).

Lightweight single-axis tracking on each branch or on the whole crown for big gains if budgets allow.

Local energy management: use small predictive controllers to schedule irrigation bursts when predicted PV production peaks.

Hybridization: combine with a small wind turbine if site windy during non-sun hours.

Optimization workflow (practical steps)

Gather site data: latitude, typical clearness index or peak sun hours, wind, max snow load (if any).

Define irrigation load profile: daily volume, peak hourly demand, pump head, required delivery schedule.

Create a CAD/parametric model of the solar tree using golden-angle placement; parameterize radial spacing, Δz, tilt.

Run shading/energy simulation across a year (hourly) and iterate geometry to maximize annual yield per installed area or per cost.

Select PV modules (normal vs bifacial), inverters/microinverters, pump, battery size (if needed).

Build a small prototype (1 trunk with 6–12 panels), monitor for 1–3 months, then scale.

Iterate after measured data.

A phyllotaxy solar tree arranges panels in a spiral pattern, inspired by leaves on plants, to capture sunlight more evenly and reduce shading. The key is choosing the right divergence angle like the golden angle (137.5°) or Fibonacci ratios (2/5, 3/8) and ensuring enough vertical spacing so panels don’t block each other. Since panels face different directions, microinverters or optimizers are needed to prevent mismatch losses. Batteries store excess energy, while smart controllers schedule irrigation pumps to run during peak solar hours. With proper geometry, electronics, and load management, phyllotaxy solar trees offer compact, reliable power for automated irrigation systems.